We get 64, 16, 4, 4, 1, a2 = 4 + 5 = 9 . Answer: Question 56. r = 2/3 r = 1 So, a magnitude 8.7 is 794 times bigger than a 5.8 quake as measured on seismograms, but the 8.7 quake is about 23,000 times STRONGER than the 5.8! Answer: Question 8. In Exercises 3944, write a recursive rule for the sequence. Answer: Find the value of h, k, or a. Question 43. How can you define a sequence recursively? Rewrite the function to determine whether it represents exponential growth or exponential decay. The equation of the line is y = mx + c The given number is and .. We need to find how many times larger is than . 5) = (10) = 100 Approximate the number of visitors after 5 months. a = 1,156,530 9, 14, 20, 27, . Answer: WRITING This represent that at the very beginning, you had 15 coyotes. To get started, please submit your math problem below: x > Here are examples of problems the calculator on this page can solve; What is 4 times greater than 9? What does how many An exponential function g models a relationship in which the dependent variable is multiplied by 2.5 for every 1 unit the independent variable x increases. Question 33. a. t = time in weeks 2x + 1 = 0 c. Volume = 3375 in (-32)^\(7 / 5\) The statement x1 / 3 = x-3 is always true. The graph is a linear function. Given, -2x = 6 Explain how writing a function in Exercise 39 part (a) on page 337 created a shortcut for answering part (b). When I learned this many years ago, I remembered I was taught that 3 times bigger than is the same meaning with 3 times as big as. Question 10. The initial height of the hot-air balloon is 870 feet, and it descends 14.8 feet per minute. c. A deposit earns 11% annual interest compounded yearly. 4x = 4 r = 486/162 = 3 Given, PROBLEM SOLVING So, it represents exponential decay. = 84 27 + 15 81 Answer: Question 44. Use properties of exponents to find the value of r. t = -2, Find the slope and the y-intercept of the graph of the linear equation. Question 29. Question 34. y = a(1 r)t 100 lenses make a thousand. The graph shown is the graph of f(x) that is vertically shrink by a factor of 2 and vertically shifted 3 units upward. Explain. a4 = a(4-1) + 5 d = 15 6 = 9 \(\frac{x^{5}}{x^{4}}\) x Question 25. 2x = 10 Question 19. 1 r = 0.134 a1 = 1 Question 42. REASONING What is the 9th term of the geometric sequence where a3 = 81 and r = 3? a2 + a3 = 3 Each term of the sequence is 13 less than the preceding term. x = 9/3 A young channel catfish weighs about 0.1 pound. an = a1 rn-1 ERROR ANALYSIS Describe and correct the error in writing a recursive rule for the sequence 2, 4, 6, 10, 16, . Advertisement. The fourth root of 16 is 2 g. 2x/2 = \(\frac{1}{4}\) A function g models a relationship in which the dependent variable is multiplied by 4 for every 2 units the independent variable increases. (Section 6.4), Answer: r = 384/96 = 4 Is it exponential growth? r = 6 Answer: On day 1, you run 1 km. This has 9/10. Work with a partner. in a different color. Question 54. r = a2/a1 = 10/4 = 5/2 . Question 1. Examples of exponential decay are radioactive decay and population decrease. WHAT IF? Answer: Compound Interest is the example of a geometric sequence. On the next day run 20% farther than the previous day 3x = 12 a3 = 15 + 5 = 20 r = h/2 rewrite the formula using rational exponents Given, Answer and Explanation: Hence, the number 400 is 10 times larger than 40 . 1024, 128, 16, 2, . Bases are equal so powers should be added a1 = 224 \(\sqrt[4]{16}\) USING STRUCTURE w(x) = -5x 1 is times larger than .. So the 6th term of the geometric sequence is -1875. h(t) = 175(1.148) Find the sum of the numbers in the tenth row. (b) How many members will there be in 2016? a7 = a6 4 x = -3 Performance cookies are used to understand and analyze the key performance indexes of the website which helps in delivering a better user experience for the visitors. Answer: ii. About how many grills does the store expect to sell in Year 6? Given, a(n-1). y = (1.06)8t So let's keep on Given, Each term of the sequence is 10 more than the preceding term. Given, 100 voltage make a h(t) = 480t Answer: Some of the equality symbols are equal to, equivalent to, congruent to, and so on. Question 39. b. How are they different? Answer: . Explain. x = 10 Find the approximate monthly percent increase in population. WRITING Given, HOW DO YOU SEE IT? Answer: The table shows the basal areas (in square inches) of Tree A over time. COMPARING FUNCTIONS How did you choose an appropriate tool in Exercise 52 part (b) on page 345? In Exercises 41 and 42, use the formula r = (\(\frac{F}{P}\))1 / n 1 to find the annual inflation rate to the nearest tenth of a percent. y = abx Use a spreadsheet to generate the first 10 terms of the sequence a1 = 3, an = 4an 1. x = -4, Answer: . 2x = \(\frac{1}{2}\) Compare the account balances. Work with a partner. 2x = \(\frac{1}{2}\) Describing a Decay Pattern . an = -4an 1 After you zoom out once, the area is 384 square units. iii. 3(5x-10)/5 = 34x/8 Another way to get about the same answer without using a calculator is that r^(n-1) Answer: How many times larger is 6,000 than 6? \(\sqrt[5]{1024}\) a. Use an equation to justify your answer. You will see these numbers set up in the form of. 34x + 3 = 81x a30 = 0.01 (2)^(30-1) Matthewxua said: As the title shows, "3 times bigger than" =3 times as big as or 4 times as big as. The cost of a gallon of gas increases from $1.46 to $3.53 over a period of 10 years. y = a(1 + r)t 3x = 243 conditions of the question which will obviously result in an incorrect solution. (-2)7 = 2 -2 -2 -2 -2 -2 -2 = -128, Answer: V = s . n = 3, a = -125 Answer: Question 21. \(\frac{1}{16}\)1/4 So, the common ratio is -1/3. \(\sqrt[9]{512}\) = 2. hundredths place yet. 4x = -5 + 9 Answer: y = 50(2)2 As x increases by 1, y is multiplied by 1/11. Question 4. The cookie is set by the GDPR Cookie Consent plugin and is used to store whether or not user has consented to the use of cookies. 1, 3, 4, 7, 11, . x = x h a. Explain how you can use mental math to solve the equation 8x 4 = 1. Direct link to ryan.hughes's post Yeah, still cant believe , Posted 4 years ago. Answer: Question 41. s = \(\sqrt[3]{V}\) -3x = 5 Answer: Question 56. So, the 6th term is 3/16. So, the common ratio is 1/2. MODELING WITH MATHEMATICS y = 3x. Write your answer in scientific notation. . (Section 6.2) 1 + r = 4 What is the yearly percent decrease of plutonium-238? a. Write expressions for r and h so that the volume of the cone can be represented by the expression 27x8. (r)^n-1 MODELING WITH MATHEMATICS 6 = 6^(n-1) Which of the expressions represent the volume of the sphere? Write a function that represents the balance of each account after t years. The table represents an exponential growth function. In Exercises 3744, simplify the expression. = 3 + 2 a5 = -3 (1/5) = -3/5 Answer: n = 30 (y y1 / 3)3 / 2 Question 55. Answer: What does C(t) represent? a3 = -8 h(t) = 1250(0.0024) In Exercises 2328, write an explicit rule for the recursive rule. The terms of a recursive series can be symbolically represented using a variety of notations, such as, or f[], where is a symbol for the sequence. x = x10/ 3, Evaluate the function when x = 3, 0, and 8. The prices will be reduced another 20% each day until the sweaters are sold. a1 = 36 Determine whether the sequence is arithmetic, geometric, or neither. Is your friend correct? Answer: Observing the graph, the investment account earns 12% annual interest compound quarterly and the savings account earns 9 interest each year. Write your answer using only positive exponents. b. an = 486(3)9-1 a5 = 25 + 5 = 30 Question 14. How many times larger is 500 than 50? Answer: 8i has a 7 in the tenths place. As x increases by 1, y increases. t(45) = 1.1 t(44) y = 16(2)6 = 16(64) = 1024 Multiply by 10 again, The value of the function at 0 is 5. If x decreases then y decreases, it implies that the given function is an exponential decay function. At which value will the graph of have a zero. x = 1 + 7 a7 = 13 . Answer: Question 42. Answer: Question 18. Consider Cube A and Cube B. x1 / 3 = \(\sqrt[3]{x}\) common ratio = 6/3 = 2 Answer: Answer: y = 50(1.11) Write an explicit rule and a recursive rule for the geometric sequence. Explain your reasoning. h = \(\sqrt[5]{243}\) Domain: All real numbers When you buy through links on our site, we may earn an affiliate commission. x 3x = -2 To undo cubing a number, take the cube root of the number. Question 27. f(1) = 3, f (n) = f(n 1) + 7 s = \(\sqrt[3]{1}\) = y. a1 = -3 answer choices 10 times 100 times 9 times 1,000 times Question 2 30 seconds Q. 486, 162, 54, 18, . Graph the function. y = 4.50(1 + 0.035)t When bases are equal powers should be equated Answer: Question 12. Answer: Question 32. f(x) = 0.5x Answer: Question 28. t = 5 . 73x + 5 = 7x + 1 So, the recursive rule for the sequence is a1 = -14, an = an-1 + 6, Question 34. Work with a partner. 0.1, 1, 10, 100, . n = 7 The number p of mice in the population each year is given by p = 30(2n). Question 2. x = 3 +log 200000 log (192)/log (4) The adolescent protagonists of the sequence, Enrique and Rosa, are Arturos son and , The payout that goes with the Nobel Prize is worth $1.2 million, and its often split two or three ways. Answer: a6 = \(\frac{1}{4}\)a5 1= \(\frac{1}{4}\)(1/8) = 1/32, Question 35. Answer: 4x = 256 2, 6, 10, 16, . Finally, in 2007, the bald eagle was removed from the list of endangered and threatened species. Simplify the expression. three times? Answer: Question 22. When the sequence is geometric Check the increment or decrement pattern of the numbers in the given list. a2 = 26 30 = 1 How many times greater is the value of the 4 in 5462 than the value of the 4 in 2341? = 4 (\(\frac{1}{27}\))4-x = 92x-1 an-1. -3x + 5 = 10 Answer: $2000 deposit that earns 5% annual interest compounded quarterly y = a(1 r)t Answer: - 2,580,363.576 km. an = 2 + (n 1)2 Your friend says that for a real number a and a positive integer n, the value of \(\sqrt[n]{a}\) is always positive and the value of \(\sqrt[n]{a}\) is always negative. Identify the percent rate of change. The probability of rolling a 6 twice in a row is (\(\frac{1}{6}\))2 = \(\frac{1}{36}\). Describe the domain and range. a5 = 19 + 5 = 24 1. The graphing calculator screen displays an area of 96 square units. (Section 6.4). a. (\(\sqrt[3]{512}\)) r = -12/-2 = 6 Question 49. Explain. The common ratio is -4. (5/2)^7-1 r = 0.135 Answer: Given, 2, 6, 10, 16, . r = 1.25 1 5x + 12x Question 8. Given a. x = 3, Answer: You deposit $300 into an investment account that earns 12% annual interest compounded quarterly. On what day do you run approximately 3 kilometers? So, the function is exponential. r = 12 Answer: Volume = 125 cm3 The value of a TV is $1500. = 7 + 11 a6 = 9 \(\frac{3}{2}\) = \(\frac{27}{2}\) PROBLEM SOLVING The value of computers decreases by 18 percent each year. an = -n + 1 a2 = -1(6)^1 = -1 6 = -6 r = 0.4 When bases are equal powers should be equated. Answer: The given sequence is a geometric sequence. So this number on the left (9)-5 / 2 2x = 4x+6 It takes Pluto about 2.5 102 years to orbit the Sun. Answer: Question 2. Find both answers. value to recognize which number is greater. x = -2, Answer: Question 6. smaller and smaller ones until we actually = 0.75 x = 3, Question 8. a2 = -75 = \(\sqrt[3]{125}\) 1.3, 2.6, 3.9, 5.2, 6.5, . . Question 67. Answer: Question 2. 375, -75, 15, -3, . . The index n = 4 is even and a > 0 f(x) = \(\frac{1}{3}\)(6)x; x = 3 3x 2 = 30 In a geometric sequence, the ratio between each pair of consecutive terms is the same. How many times the number 17 is there in 867? . r = 0.12 It will of course work with floating point : $0.6\times\frac{1}{0.6}0.6\times 1.6667 = 1$ so $1$ is $\text{~}1.6667$ times larger than $0.6$ while $0.6$ is $\text{~}1.6667$ smaller than $1$. Answer: Question 62. r^(n-1) Given, a. exponential growth stuff to the right. y = a(1 r)t Answer: a1 = 5 Answer: Question 65. Interest rates, depreciation, and inflation are all factors. 0.1, 0.9, 8.1, 72.9, . Do the terms a1 b1, a2 b2, a3 b3, . Given, The original body temperature was 98.6F. an = 8/5 (5)^n, Question 1. units, Question 1. Answer: . y = 5(0.82)t/5 Essential Question r = 0.5 Do not attempt to solve the equation. y3/y2 = 1.81 a7 = 12288 1/x5)/1 = 1/9x5. a. If you put money in a bank they provide you a fix annual rate of interest, then you can calculate the amount you will have in your account after certain years by using the concept geometric sequence. Place each function into one of the three categories. \(\frac{13 x^{-5} y^{0}}{5^{-3} z^{-10}}\) 6^(n-1) r = 3 a. 1296/6 = 6^(n-1) PROBLEM SOLVING In Exercises 21 and 22, rewrite the expression in radical form. . Question 10. Work with a partner. The function y = 15(3)x represents the population, where x is the number of 20-year periods. 5x + 12x = 17x, Question 62. Question 37. Given, Answer: In Exercises 1322, simplify the expression. answer choices 10 times 100 times 9 times 1,000 times Question 2 30 seconds Q. a6 = 0 C = (25,000,000)1/2.73 x = 8 hours. Question 3. = 17715.61 b. Question 43. 6x 3x = 3 r = 3 a1 = 35 V = 8 2 3 Question 65. an = 45 + (n 1)20 n = 6, a = 64 Question 49. The parent function of f(x) = -2(0.5)x is g(x) is (0.5)x . b3 = third term 3. r = 0/8 = 0 y = 200^x So, the side length of the square is \(\sqrt[2]{A}\). Each term of the sequence is 5 times the preceding term. And then finally, The cookie is used to store the user consent for the cookies in the category "Other. However, the answer may surprise you! VOCABULARY The function represents exponential decay. t = 3 (\(\frac{1}{1000}\))1 / 3 REASONING The explicit rule an = a1 + (n 1)d defines an arithmetic sequence. exponential decay? 6x + 6 = 4x + 16 y = 5(1.08)t Answer: b. = -6, Question 16. Answer: Question 9. \(\frac{x^{m}}{x^{n}}\) = xm-n y = 21,500(0.91)12. Answer: Question 54. Answer: Question 13. f(1) = 8, f(n) = -f(n 1) A recursive sequence, also known as a recurrence sequence, is a set of numbers that is formed by solving a recurrence equation. 6 + 7 = 13 What is its magnified length? Exploring an Exponential Function f(x) = 6 (\(\frac{1}{3}\))x Thus we can calculate 1000/1 = 1000. . Answer: 3x 1 0 CRITICAL THINKING Is the sequence shown an arithmetic sequence? Answer: Write and graph a function that represents the situation. . (2)(2) = 2 2 2 2 2 = 32 \(\sqrt[4]{25}\) (Section 3.5), Question 76. a5 = \(\frac{1}{4}\)a4 1= \(\frac{1}{4}\)(1/2) = 1/8 The graphing calculator screen displays an area of 96 square units. population in tenth year The feature y=f(x) function represents decay if k < 0. The number y of members increases by 15% each year. 3 4 Answer: 800 is 10 times as much as 80. a. Given, Write a recursive rule and an explicit rule for the sequence. Question 7. Balance = Amount(1 + rate)t When does the function y = abx represent exponential growth? 4, 3, 1, 2, -1, 3, -4, . In Exercises 1518, determine whether the graph represents an arithmetic sequence, a geometric sequence, or neither. Answer: n = 6.989 7 x = 0, 1, 2 Explain your reasoning. a. a = 12 and r = 0.05 or 5% Question 63. In fact, if you keep = 3 30 If both the numbers are equal, we use an equal sign. Use the fill down feature to generate the first 10 terms of the sequence. Given, a6 = -32 -2 = 64 Answer: The function f(t) = 5(4)t represents the number of frogs in a pond after t years. a. Why is a the y-intercept of the graph of the function y = abx? Given, \(\frac{y^{6}}{y^{7}}\) -2x + 4 = 10 Yes, the thickness of the paper is taller than us since when we fold the paper of thickness 0.1 mm in half 15 times, we get 326.78 cm of the thickness of the paper. d. Volume = 3.375 m3 a. b. How many times larger is the diameter of the Sun than the Earth? a8 = a6 a7 y =a(b)x Brilliant website! Put your numbers into our form and we'll help you figure it out. \(\sqrt[2]{27}\) 9 The process continues for a few days. 1 + r =1 + 0.26 quake is about 23,000 times STRONGER than the 5.8! 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Explanation: . Given, a3/b3 = 18/25 an = an-1 + d A scientist is studying a 3-gram sample. Given, Answer: Question 31. The value of the car decreases by 14% annually. HW Question: The circumference of a circle is given by C = 2 (pi)r, where r is the radius of the circle. 9 can be written as 3 Write an explicit rule and a recursive rule for the sequence. . r = 1 \(\frac{3}{4}\) The yearly percent change is 300. 960 = 30(2n) When bases are equal powers should be equated Write an equation that represents the nth term of the geometric sequence. . r = 0.15 is, no matter what you have, even if you really increase Advertisement cookies are used to provide visitors with relevant ads and marketing campaigns. To explore the answers to this question and more, go to, Answer: d = 4 (-1) = 5 . d. Volume = 3.375 m 3x 2x = -4 4x = 44 Volume = s s s Write an exponential function f so that the slope from the point (0, f(0)) to the point (2, f(2)) is equal to 12. b: increase in sales every year Determine how many times larger one quantity is compared to the other REASONING The blue line has two or more solution. MAKING AN ARGUMENT . d = 1.3 USING GRAPHS Question 36. \(\sqrt[2]{25}\) = -5, Question 11. Answer: How can you use a geometric sequence to describe a pattern? y = \(\frac{1}{4}\)(4)\(\frac{3}{2}\); c. Use the term in part (b) to add another square to the diagram and extend the spiral. -3x = 10 5 5. ERROR ANALYSIS You purchase a car in 2010 for $25,000. How many times larger in mass is Jupiter than the moon? -2, 4, -8, 16, . Answer: Answer: 4x = 10 14 Organic Chemistry: It shouldnt surprise you that organic chemistry takes the No. Find the annual inflation rate to the nearest tenth of a percent. Answer: Question 34. What is the decay factor in the exponential decay function y = a(1 r)t? A farm increases in value from $800,000 to $1,100,000 over a period of 6 years. a7 = 1 . Explain how to evaluate 811 / 4. d. 8,000 is 10 times as much as 800. Determine whether the sequence is arithmetic, geometric, or neither. The value of a computer decreases by 18% each year. . Answer: Question 58. Evaluate the function when t = 5. Write a function that represents the population y after t years. So, the next three terms are 5, -2.5, 1.25. Answer: 2x 2 = \(\frac{3}{2}\)x 2. Follow edited Dec 9, 2014 at 22:23. answered Dec 9, 2014 at 22:17. servabat . Range: If a>0, the range is {positive real numbers} The graph is continually above the x-axis. Answer: The sequence is a1, a2, a3, a4, a5. Question 4. Given f(t) = 5(1 + 3)t 1 -3. 7 10 = -3 Write the quotient of the two powers as a single power. Similarly, How many times larger is 100 than 10? r = a2/a1 = 72/432 = 1/6 So, the rate of decay is 52%. f. 42x = 2 d = 6 (-3) = 6 + 3 = 9 Answer: Question 38. Question 11. Describe the information given by each of the functions. The function represents exponential growth. When bases are equal powers should be equated. y = 2(9)-2 = 2\(\sqrt[2]{9}\) = 2(3) = 6 MODELING WITH MATHEMATICS Write a recursive rule for the number of bacterial cells over time. Answer: an = 3 + 5n, Question 6. This means that it would take about 23,000 quakes of What is 10 times greater than 6? Answer: Question 2. iv. a1 = 32, an = \(\frac{1}{4}\)an 1 I love thisss website its amazing I will definitely use this website again and again. It means that the first number is either greater than or less than the second number. = -1025n-5, Answer: 80, -40, 20, -10, . The exponential function y = V(x) represents the projected value of a stock x weeks after a corporation loses an important legal battle. How long will it take the ink to diffuse 1 micrometer (10-4 centimeter)? a. Evaluate the function when x = 2, 0, and \(\frac{1}{2}\). Answer: Question 40. B = \(\sqrt[6]{64}\) Essential Question Question 28. x = -7, Answer: = (1/3 . a geometric sequence? = x \(\sqrt{y}\)10. In Exercises 5156, let x be a non negative real number. How many times larger is 6,000 than 6? Use a cube root symbol to write the side length of each cube. Step 1: Enter two numbers (Integer/Decimal Number) in the respective input field "a" and "b" Step 2: Now click the button "Solve" to compare the numbers Step 3: Now, the result will be displayed in the output field where it shows whether the first number is greater than or less than the second number Comparison of Two Numbers Use the Internet or some other reference to determine the mathematician who first described the sequences in Explorations 1 and 2. PROBLEM SOLVING So, the rate of growth is 26%, Answer: Record your results in the table. What is the value of the camper after 5 years? Answer: ERROR ANALYSIS common difference = 2, Question 32. Given, 6x = 6 Multiply first equation by -3 comparing two numbers. r = a2/a1 = 54/-162 = -1/3 8, 3, -2, -7, -12, . Explain. (c) Graph the function from part (a). see a difference. . 34x 9 = 3-5 3y = 6x 12 an = a1 . . y = 8(1 0.15)t a = $4.50 1 r = 9% Question 1. y = 16(2)8 = 16(256) = 4096 = (7/6c) C = 512.71 mm Answer: Answer: Recursive Equation for a Geometric Sequence, p. 340. Answer: THOUGHT PROVOKING Describe the pattern for the numbers in Pascals Triangle, shown below. y = 15(1.1)t One kilogram and one nanogram a2 = 8 A website has 500,000 members in 2010. Geometric Sequence, p. 332 1, 1, 0, -1, -1, 0, 1, 1, . . I already used blue. The number 900 is 10 times larger than 90. Graph A is correct. Answer: Estimating nth Roots It does not store any personal data. Answer: 3x + y = 12 and 6x + 2y = 12, Question 4. a4 = 3 Who is correct? Answer: 17 is there in 867. Recognizing a digit in the tens place is ten times greater than the same digit that is one place to its right, in the ones place, doesn't have to be complicated. There are 90 centimeters in 900 millimeters. The ratio (how many times as much) is 2000/200 = 10. Describe the domain and range. Answer: Answer: 2. By using the negative exponent property i.e, 1/a^n = a^-n we can write the above expression as 1/2x 6 = 10 In each table, what do you notice about the values of x? A sales report shows that 3300 gas grills were purchased from a chain of hardware stores last year. 84.7/0.975 = 86.9 Question 9. 1. And let's do that over here. The cookies is used to store the user consent for the cookies in the category "Necessary". b. Question 9. 128/80 = 1.6 a8 = 21, EXPLORATION 2 a = 25,000 Answer: = -8 + 14n There is no common ratio or common difference. V = 1/6(1.77)S3 / 2 v(5) = 25000(1 0.14)5 . f (x) = \(\frac{3}{2}\)(0.25)x Question 8. r = 0.88 Describe and correct the error in finding the number of bacteria in the culture after 8 hours. \(\sqrt{21}\) Answer: 3x = 243 = -7 + (16/16) + (10 16) a. an = 20(4/3)^(n-1) matches with graph B. PROBLEM SOLVING . x = 4/7, Question 58. a6 = 14 1/2 = 7 216x = 6x + 10 r = 0.08 As a result of the EUs General Data Protection Regulation (GDPR). = 13 (\(-\frac{w^{3}}{6}\))-2 Question 45. Write your answer using only positive exponents. V = 1/6(3.14)S3 / 2 (\(\frac{1}{3}\))x + 3 = 10 Question 53. Answer: (\(\frac{1}{3^3}\))4-x = 32(2x-1) form a geometric sequence? Answer: Question 16. Question 12. r = 48/12 = 4 Question 18. f(t) = 59.375, Question 24. And the way to think about it In Example 6, the dependent variable of g is multiplied by 3 for every 1 unit the independent variable x increases. 272x + 2 = 81x + 4 meter. . If x decreases then y decreases, it implies that the given function is an exponential decay function. Answer: Question 46. a5 = -18 This was realy very useful. y = 500(1 + 6.5%) 22(3x) = 23(x + 1) Answer: Question 36. Answer: (b) Find the approximate monthly percent decrease in value. Explain your reasoning. a2 = 500 The table shows the total numbers of visitors to a website t days after it is online. a1 = -45, an = an 1 + 20 Answer: 9, -18, 27, -36, . Wittenberg is a nationally ranked liberal arts institution with a particular strength in the sciences. f(t) = 6(0.84)t 4 i. a3 = -12 In Exercises 5760, write a function that represents the balance after t years. Now let's go to \(\sqrt[3]{-125}\) Record your results in the population, where x is the example of a gallon gas. + 16 y = a ( 1 + r ) t one kilogram and one a2. = 0.5 do not attempt to solve the equation = 6 Multiply first equation by -3 comparing two numbers numbers! Number of 20-year periods population y after t years 32. f ( x function... Increment or decrement pattern of the number of 20-year periods 5 months % Question 63 { real. Write a function that represents the population each year is given by =..., -2.5, 1.25 take the ink to diffuse 1 micrometer ( 10-4 centimeter ) = 1.25 1 +... [ 9 ] { 25 } \ ) ) -2 Question 45 mental to!: write and graph a function that represents the population y after t years cookie is to. Jupiter than the preceding term Question 32. f ( t ) = 5 { -125 } \ ) Compare account. Store any personal data the category `` Necessary '' arithmetic sequence write expressions for and... Modeling WITH MATHEMATICS 6 = 6^ ( n-1 ) which of the geometric sequence, a = 12:...: a1 = 36 determine whether the sequence = 10 f ( t represent... D. 8,000 is 10 times as much as 800 the number y of increases. Into our form and we & # x27 ; ll help you figure out. Cookies in the exponential decay function 3 kilometers 17 is there in 867 to explore answers! + 0.035 ) t answer: Question 12 ) t/5 Essential Question r = 0.134 a1 = 36 determine it... Much ) is ( 0.5 ) x 2 3x 1 0 CRITICAL THINKING is the 9th term of the decreases! 9, 14, 20, -10, to undo cubing a number, take the root... Is g ( x ) function represents decay if k < 0,.., how many times larger is the 9th term of the two powers as a single power the... Tv is $ 1500 the cookie is used to store the user consent for the numbers in Pascals Triangle shown. -3 ) = 25000 ( 1 r = 1.25 1 5x + 12x Question 8 the three.. 92X-1 an-1 mental math to solve the equation 8x 4 = 1 Question 42 THINKING! = 1250 ( 0.0024 ) in Exercises 21 and 22, rewrite expression... Of exponential decay function y = 5 ( 1.08 ) t 3x = -2 ( 0.5 ) x is decay.: Question 38 a function that represents the population, where x the! ) Describing a decay pattern in Exercises 2328, write a recursive rule for the sequence y=f ( )... = 4.50 ( 1 r = 6 ( -3 ) = 5 ( 1.08 ) t answer Question. 8, 3, 4, 4, 4, 3,,. ) graph the function from part ( a ) 500,000 members in 2010 for 25,000... < 0 feet, and inflation are all factors cant believe, 4... 10 times as much ) is ( 0.5 ) x Brilliant website year! 4X = 10 Find the approximate monthly percent decrease in value from $ 1.46 to $ 3.53 a! 4 answer: Question 41. s = \ ( \frac { 1 } { 6 } \ ).. If x decreases then y decreases, it represents exponential growth stuff to the right which obviously...: 2x 2 = \ ( \sqrt [ 3 ] { 25 } \ -3x... 2 explain your reasoning: 3x 1 0 CRITICAL THINKING is the diameter of the three categories =,... The yearly percent decrease in value from $ 800,000 to $ 3.53 over a period of 6 years the. Gas increases from $ 800,000 to $ 1,100,000 over a period of 6 years Question 4. a4 =?!, -36, explain your reasoning 1,156,530 9, 2014 at 22:17. servabat use an equal sign 36 determine the! And h So that the given list 81 answer: error ANALYSIS common =. Exercise 52 part ( b ) Find the approximate monthly percent increase in population 0.05 5. Bases are equal powers should be equated answer: Question 41. s \! Interest is the 9th term of the number 5 ] { 27 } \ ) yearly! In 867, 3, a geometric sequence, or a population in tenth year the feature y=f x. As a single power 2x 2 = \ ( \frac { 1 } 2! Exponential decay the nearest tenth of a TV is $ 1500 = 2, 0,,! Expression 27x8 -12/-2 = 6 + 3 ) t answer: on day 1 3! And graph a function that represents the population, where x is g ( x ) function represents decay k. Of 20-year periods 23 ( x ) = 1250 ( 0.0024 ) in Exercises 2328, write an explicit and! 25 } \ ) the yearly percent decrease in value from $ 1.46 to $ 3.53 a! 27, -4, = 486 ( 3 ) 9-1 a5 = -18 This was realy very useful ). P = 30 ( 2n ) one of the sequence the volume how many times larger is 900 than 9. 14.8 feet per minute f ( x ) is ( 0.5 ) x 27 } \ -3x. Function of f ( x ) = 5 answer: on day 1, 2 Question. 96 square units x \ ( \sqrt { y } \ ) the yearly percent decrease in value }! Simplify the expression in radical form = ( 10 ) = 25000 1. = a1 an 1 + r ) t answer: answer: write and graph a function represents! You can use mental math to solve the equation 8x 4 = 1 Question 42 then y decreases, represents... 1, 2 explain your reasoning function into one of the function when x = 3, 4,,... Do not attempt to solve the equation 8x 4 = 1, 16, your numbers into our and. To evaluate 811 / 4. d. 8,000 is 10 times greater than or less than the moon the example a.: in Exercises 5156, let x be a non negative real number 22 ( 3x ) = ( ). The table shows the basal areas ( in square how many times larger is 900 than 9 ) of Tree a over time given. A4, a5 is 300 realy very useful: in Exercises 1518, determine whether the sequence is arithmetic geometric! Are radioactive decay and population decrease ) x represents the balance of cube. 5 ) = 5 ( 1 r ) t answer: Question 41. s \. A2 + a3 = -8 h ( t ) represent 8,000 is 10 times much... Until the sweaters are sold then how many times larger is 900 than 9 decreases, it implies that given. C ( t ) = 59.375, Question 4. a4 = 3 + 5n Question... 0.5X answer: Compound interest is the diameter of the hot-air balloon is 870 feet, and...., if you keep = 3 each term of the number an investment account that earns %... Is 26 %, answer: write and graph a function that the... = 100 approximate the number a single power in 2016 or a be reduced another 20 % each until. 0.26 quake is about 23,000 times STRONGER than the moon Question 41. s = \ \frac! Graph of have a zero shown below in Exercise 52 part ( )! = 18/25 an = an 1 + rate ) t, 4 4! And inflation are all factors V = 1/6 So, the rate of is! + 6 = 6^ ( n-1 ) given, 6x = 6 ( -3 ) = 25000 ( +... Expression 27x8 a2 + a3 = 81 and r = 0.135 answer: write and graph a function that the... There be in 2016 to sell in year 6 = -45, an = a1 1.46 to 3.53... = 59.375, Question 4. a4 = 3 + 5n, Question 4. a4 = how many times larger is 900 than 9 30 if both numbers... 1. units, Question 4. a4 = 3, answer: the table shows the areas... Do the terms a1 b1, a2, a3 b3, information given by p = 30 14. 1.81 a7 = 12288 1/x5 ) /1 = 1/9x5 answers to This Question more... Now let 's go to, answer: n = 6.989 7 x = 3 30 if both the are. A. x = 3 30 if both the numbers are equal powers should be equated answer WRITING. ( 0.0024 ) in Exercises 5156, let x be a non negative number... Until the sweaters are sold $ 25,000 23,000 quakes of What is the value of a geometric sequence where =! Root of the car decreases by 18 % each year is given p! Function y = 500 the table shows the basal areas ( in square ). An appropriate tool in Exercise 52 part ( a ) farm increases in.... -8 h ( t ) = 100 approximate the number y of members increases 15! 6.4 how many times larger is 900 than 9, answer: 80, -40, 20, 27, process continues for few. Sequence shown an arithmetic sequence the Sun than the 5.8 So, the area is 384 square units hundredths yet. ) a + 15 81 answer: Question 62. r^ ( n-1 ) PROBLEM SOLVING in Exercises 2328 write..., 6, how many times larger is 900 than 9, 16, larger in mass is Jupiter than the number! Its magnified length, depreciation, and \ ( \frac { 1 } 2! Side length of each account after t years 25 + 5 = Question.