Given, a. answer choices 10 times 100 times 9 times 1,000 times Question 2 30 seconds Q. b. y = 2(3)x EXPLORATION 3 y = 300(1 + 12/100)4t n = 7 a1 = 0, an = an 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. Why are t statistics more variable than z scores. Property of Equality for Exponential Equations, p. 326 r = 3 and g(x) = 0.25^x + k = 243 y 5 = m(x + 3) For this we need to divide it by 17 and the answer comes is 867/17=51. Check your answer. Section 6.5 a5 = 1.5a5 1 = 1.5(27) = 40.5 3, 12, 48, 192, . The cookie is used to store the user consent for the cookies in the category "Performance". = 1/4xy8, Question 5. = -7 + 1 6 a1 = 0.1 PROBLEM SOLVING 1, -5, 25, -125, . Answer: an = -3an 1 In the grammar books I read, all agrees that 3 times bigger than means 4 times as big . Answer: In Exercises 2332, simplify the expression. Given, Answer: It represents exponential growth. a. Place each function into one of the three categories. d. 8,000 is 10 times as much as 800. Answer: d = 2 As x increases by 3, y decreases by 9. Find and interpret the y-intercept. y = 422.5(0.714) Answer: . 1 (-3) = 4 93.7/0.975 = 96.1 To score above 90 marks in chemistry, practising CBSE Class 12 sample papers are essential. x = 1500 0.86 Binary acids are all written in H-A form, which means hydrogen bond to a nonmetal atom. . So, the next three terms are 73, 118, 191. a7 = a5/a6 Explain how writing a function in Exercise 39 part (a) on page 337 created a shortcut for answering part (b). r = 1.1 1 b. If the numbers are the same, continue to smaller place values until we find a difference. 52y8/22x4 r = 26/13 When bases are equal powers should be added. Question 53. \(\frac{2^{-4}}{4^{0}}\) a4 = 20 + 5 = 25 What place is the 4 in the number 34,865? Given, a1 = 32, an = \(\frac{1}{4}\)an 1, Answer: What is 10 times greater than 6? The first term of a sequence is 8. Question 35. Question 37. The area of the rectangular computer chip is 1123b2 square microns. 17,000 = 4/3 3.14 r The function f(t) = 5(4)t represents the number of frogs in a pond after t years. a25 = 0.01 (2)^(25-1) REASONING v. f(x) = 1/2x 6 c. Volume = 3375 in A deposit earns 11% annual interest compounded yearly Question 55. Answer: Question 58. Given, y = 410 t = t/12 1 r = 1.08 y = 2(9)x Then enter =A1+2 into cell A2, as shown. Is your friend correct? A bacterial population y after x days can be represented by an exponential function whose graph passes through (0, 100) and (1, 200). Answer: Question 56. Answer: Question 26. Given, 3. r^(n-1) Determine whether the function represents exponential growth or exponential decay. Answer: y = 500(0.82) The y-intercept occurs on a graph when x = 0. Given, Write your answer using only positive exponents. Justify your answer. b. Graph the functions from part (a) in the same coordinate plane. \(\frac{x^{4}}{x^{7}}\) EXPLORATION 1 Question 1. (a) Write a function that represents the population. The number y of members increases by 15% each year. a1 = 45 r = 3.5% or 0.035 r = a2/a1 Answer: y = 50(2)3 The given statement is wrong. r = -3 Equation for a Geometric Sequence, p. 334, Section 6.7 Your school is conducting a survey. a1 = 4, an = an 1 + 5 answer choices 1,000 times 1 time 10 times 100 times Question 4 30 seconds Q. Answer: r = 0.15 (b) How many members will there be in 2016? n = 5 a1 = 5, an = an 1 4 COMPLETE THE SENTENCE A recursive rule gives the beginning term(s) of a sequence and a(n)_____________ that tells how an is related to one or more preceding terms. Although a minimal amount of carbohydrate digestion occurs in the mouth, chemical digestion really gets underway in the stomach. Graph the function f(x) = -2x. 6, 1, 7, 8, 15, 23, . 17716. So helpful for my school work, would defiantly use again. Question 41. So, after 10.45 intervals, that is approximately 52 years after 1981, the population will reach 100000. The function f(t) = 5(4)t represents the number of frogs in a pond after t years. Learn More. actually add up these numbers and compare them as fractions. a7 = 15625/16 a6 = a5 + a4 The population of a year is 60% greater that the population of the previous year. (See Example 1.). 1. a2 = -75 f(x) = \(\frac{1}{3}\)(6)^x And so what is this Question 3. y = P(1 + r/n)nt So, the next three terms are -3/5, -3/25, -3/75. After you zoom out a second time, the area is 1536 square units. 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. a = 1,156,530 . Domain: All real numbers About how much will the catfish weigh after 4 weeks? So no matter how you think Question 11. Select two equations to support Student As claim. f(1) = 10, f(2) = 15, f(n) = f(n 1) f(n 2) r = 25% You deposit $500 in a savings account that earns 9% annual interest compounded monthly. r = 5 What is its magnified length? an = -1(6)^(n-1) REASONING What is the 9th term of the geometric sequence where a3 = 81 and r = 3? Answer: -6d 7, Write a linear function f with the given values. A milligram and a hectogram Plutonium-238 is a material that generates steady heat due to decay and is used in power systems for some spacecraft. Explain your reasoning. \(\sqrt[3]{125}\)= -5, Question 2. \(\sqrt[3]{8}\) = 2, Question 6. Answer: Question 69. Given, (\(\frac{1}{1000}\))1 / 3 As the x values increases by 1, the y decreases by a division of 4. a7 = 432(1/46656) (-64)1 / 2 WRITING a3 = 5 c. Answer: In Exercises 4548, simplify the expression. y = 16(2)6 = 16(64) = 1024 a7 = 2500(1/5)^6 = 2500/15625 = 0.16 She will pay her parents $0.01 for the first day of the month, $0.02 for the second day, $0.04 for the third day, and so on. a3 = 56 Work with a partner. Answer: Question 19. n = 3 2x = 2 \(\sqrt[3]{-125}\) a. Answer: y = 21500(1 0.09)12 EXPLORATION 1 Answer: Question 36. MODELING WITH MATHEMATICS a1 = 1 (r)^(n-1) a7 = -4 = Equal To This is the equal to operator. Answer: Properties of Exponential Decay Functions k = 4 1 (r)^n-1 By clicking Accept, you consent to the use of ALL the cookies. Answer: Then graph the sequence. How many digits answer we will get when we add 99 and 1? This cookie is set by GDPR Cookie Consent plugin. 3, 9, 27, 81, 243 Round your answer to the nearest thousand. a = 1250 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? Answer: 128/80 = 1.6 x = -12 2, 8, 32, 128, . P = 1400 s = 5 cm. ERROR ANALYSIS So, the common ratio is 3. There are 90 centimeters in 900 millimeters. Question 1. . an = a1 + (n 1)d An exponential function h models a relationship in which the dependent variable is multiplied by \(\frac{1}{2}\) for every 1 unit the independent variable x increases. (r)^n-1 Write an equation that represents the nth term of the sequence. = -1/1/2 = -2 = -4, Question 4. b. The common difference is 7. The parent function is g(x) = (\(\frac{1}{3}\))x. (x/2) = x/2 = x/8. 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 Answer: The value of the car in 2015 is not about $48,000 it is about $12,000. Answer: Cite. Answer: Question 54. 1 + k = 4 Question 34. As x increases by 1, y is divided by 1.5. = 0.75% . Answer: EXPLORATION 3 b. Student B claims she can form a linear system from the equations shown that has one solution. WHICH ONE DOESNT BELONG? You store blankets in a cedar chest. An infinite geometric series is the sum of an infinite geometric sequence. r = a2/a1 y = 500(0.845) r = -1/2 b. = 25y8/4x4, Question 5. How long does it take sunlight to reach Jupiter? a1 = 2500 Use the percent decrease found in part (a) to make a table showing the decreases in body temperature. 3(5x-10)/5 = 34x/8 Answer: What is the volume of the cedar chest? 839/524 1.6 -12 + 3x = 4x 2 a10 = 1 . So, Answer: The total number of rabbits each month follows the exponential pattern 2, 4, 8, 16, 32,. . = (-4) The Number of Solutions of an Exponential Equation x = 4 Horizontal Asymptote: when b>1, the horizontal asymptote is the negative x-axis, as x will become a huge negative. r = 0.52 Question 7. What power of 2 represents the number of different ways that a student can answer all the questions in Part 1? y = 4681.11 \(\frac{3}{49}\), \(\frac{3}{7}\), 3, 21, . an = a1 rn-1 When we fold it three times then the thickness of the paper is 0.4 2 = 0.8 millimeter Do you think the statement below is true for any exponential function? r = [(\(\frac{F}{P}\))1 / n 1] 100 (\(\frac{1}{3}\))2x (\(\frac{1}{3}\)) = 5 f(4) = 1280. t = -2, Find the slope and the y-intercept of the graph of the linear equation. a. 4/2 = 2 2x = 2-7 5) = (10) = 100 magnitude 5.8 to equal the energy released by one magnitude 8.7 event. Answer: a2 = 48 Determine whether the table represents an exponential growth function, an exponential decay function, or neither. Answer: a5 = a(5-1)+5 Organic Chemistry: It shouldnt surprise you that organic chemistry takes the No. = \(\sqrt[4]{256}\)5 = 27. D. The hot-air balloon descends 14.8 feet per minute. Given, 10**1.5 times) the energy, based on a long-standing empirical formula that = -5, Answer: Given, an = 0.01 (2)^(n-1) y = 50(2)2 x = 3, Answer: A $900 sound system decreases in value by 9% each year. a6 = a5 r b. r = 1.05 1 HOW DO YOU SEE IT? y = 500(1 + 0.065). . 3 = 0 a2 = 1 Question 45. Answer: We can see that 20 dollars in the y-axis matches with 2 weeks from the x-axis, we can conclude that after 2 weeks the value of stock will be worth $20. Answer: The cookie is used to store the user consent for the cookies in the category "Other. common difference = 1/4 a2 = 0.9 Answer: Question 66. = 3435 n = 9 y = 16(2) = 16(4) = 64 MODELING WITH MATHEMATICS a4 = 28 Does the table represent a linear or an exponential function? After you zoom out once, the area is 384 square units. x = x h Answer: Answer: Fifth root of 32 is 2 number on the right. y is multiplied by a constant factor, the function is not exponential. 2. c. Graph the function from part (a). Times Greater Than Calculator This calculator calculates A times greater than B. You graph an exponential function on a calculator. -20x = 40 \(\sqrt[5]{1024}\) Question 16. 9a 9-b = 9a-b, Question 16. Answer: Question 42. So plus 8/1000. Answer: -12 + 2 = 4x 3x 9 x 10^5 is 1.8*10^2 larger than 5 x 10^3.. What is exponents and power? Answer: Question 64. a1 = 32 Identify the percent rate of change. 4, 20, 100, 500, 2500, . y = 5(0.82)t/5 a1 = -5 x = 1. y = 5(0.82)t/5 a2 = 12 Play this game to review Other. \(\sqrt{4}\) = \(\sqrt{2}\) = -2, Question 6. r = -15/-75 = 1/5 Answer: Question 34. Explain your reasoning. 2x-7 = 27 r = common ratio = (1/3 . . Answer: r = 384/96 = 4 Answer: Answer: Answer: Question 12. The value of the function at 0 is 8. = 5(1 + 0.12246)t = b-5 b8 = b-5+8= b, Question 6. a2 = 6 a3 = a(3-1) + 5 1, 3, 5, 7,. Answer: Question 50. d = -18 + 25 = 7 Direct link to Hira Umar's post I am a professional at de, Posted a year ago. Answer: Answer: Write an explicit rule for the recursive rule. Answer: Ten times greater Step-by-step explanation: In order to calculate this you just have to divide the 9,000 between the 900 to see how many times greater it is the value of the 9 in 9000 than the value of 9 in 900: . Question 63. (\(\frac{1}{8}\))5x = 32x+8 Given, 4x x = 9 Consider Squares 16 in the diagram. PROBLEM SOLVING . The probability of rolling a 6 on a number cube is \(\frac{1}{6}\). . The domain of -(0.5)^(x 1) is all real numbers whereas range of -(0.5)^(x 1) is y < -1 OPEN-ENDED Write a geometric sequence in which a2 < a1 < a3. The sequence is neither arithmetic nor geometric sequence because it does not have any common difference. The graph shown is the graph of f(x) that is vertically shrink by a factor of 2 and vertically shifted 3 units upward. (b) Find the approximate monthly percent decrease in value. Once again, 9 is 9000/1000, -2x = 6 The table represents an exponential growth function. Answer: Essential Question 1. How long will it take the ink to diffuse 1 micrometer (10-4 centimeter)? Answer: Question 20. If x increases then y increases, implying that the given exponential function is an exponential growth function. . s = \(\sqrt[3]{V}\) Answer: Describe and correct the error in evaluating the function. Write your answer in scientific notation. a2 = 100 = 400/4 = 100 Answer: Describe and correct the error in finding the number of bacteria in the culture after 8 hours. Explain. a6 = 81 . Answer: Question 11. Then, as you know, you can always add a zero after the decimal point and it won't change the value of the number. how we get that number: One whole unit of magnitude represents approximately 32 times (actually y5/y4 = 1.34 y = abx Question 28. 3-x 1 is a horizontal translation. The initial amount = $35,000 f(x) = 2x 4 3 . an = a1 + (n 1)d Answer: -3, -4, -7, -11, -18, . a = 500,000(1.15)^6 y = 200^5 What is the probability of rolling a 6 four times in a row? Question 20. PROBLEM SOLVING b > 1 1, 3, 9, 27, . Given, 432, 72, 12, 2, . Answer: Question 9. r = 18/100 Assume that the original body temperature was 98.6F. r = 12 t(46) = 1.1 t(45) How do you calculate how many times greater something is in scientific notation? You purchase a car in 2010 for $25,000. The function represents exponential decay. Answer: Answer: Given, y = 1.5(2)x r = a2/a1 3y = 6x 12 PROBLEM SOLVING T = 128 (1/2)n Answer: USING TOOLS You can use a spreadsheet to generate the terms of a sequence. (\(\frac{1}{3^3}\))4-x = 32(2x-1) a1 = 16, an = 0.5an 1 d. Is it possible for an exponential equation to have no solution? So, the function that represents this situation is 1500 0.86^t = x, the monthly percent decrease is 0.16% and after 3 years the car will be valued at $954.08, Answer: Question 51. Write functions that represent the balances of the accounts after t years. 7, 6, 13, 19, 32, . Answer: 3x + y = 12 and 3y + 9x = 36 Answer: (a) Write a function that represents the value y (in dollars) of the TV after t years. Answer: Question 9. (, Exponential Functions and Sequences Maintaining Mathematical Proficiency Page 289, Exponential Functions and Sequences Mathematical Practices Page 290, Lesson 6.1 Properties of Exponents Page(291-298), Properties of Exponents 6.1 Exercises Page(296-298), Lesson 6.2 Radicals and Rational Exponents Page(299-304), Radicals and Rational Exponents 6.2 Exercises Page(303-304), Lesson 6.3 Exponential Functions Page(305-312), Exponential Functions 6.3 Exercises Page(310-312), Lesson 6.4 Exponential Growth and Decay Page(313-322), Exponential Growth and Decay 6.4 Exercises Page(319-322), Exponential Functions and Sequences Study Skills: Analyzing Your Errors Page 323, Exponential Functions 6.1 6.4 Quiz Page 324, Lesson 6.5 Solving Exponential Functions Page(325-330), Solving Exponential Functions 6.5 Exercises Page(329-330), Lesson 6.6 Geometric Sequences Page(331-338), Geometric Sequences 6.6 Exercises Page(336-338), Lesson 6.7 Recursively Defined Sequences Page(339-346), Recursively Defined Sequences 6.7 Exercises Page(344-346), Exponential Functions and Sequences Performance Task: The New Car Page 347, Exponential Functions and Sequences Chapter Review Page(348-350), Exponential Functions and Sequences Chapter Test Page 351, Exponential Functions and Sequences Cumulative Assessment Page(352-353), Big Ideas Math Answers Grade 7 Accelerated, Bridges in Mathematics Grade 2 Home Connections Unit 1 Module 4 Answer Key, Bridges in Mathematics Grade 2 Home Connections Unit 1 Module 3 Answer Key, Bridges in Mathematics Grade 2 Home Connections Unit 1 Module 1 Answer Key, Bridges in Mathematics Grade 4 Student Book Unit 8 Module 3 Answer Key, Bridges in Mathematics Grade 4 Student Book Unit 8 Module 4 Answer Key, Bridges in Mathematics Grade 5 Student Book Unit 5 Module 1 Answer Key, Bridges in Mathematics Grade 5 Student Book Unit 5 Module 2 Answer Key, Bridges in Mathematics Grade 5 Student Book Unit 5 Module 3 Answer Key, Bridges in Mathematics Grade 5 Student Book Unit 5 Module 4 Answer Key, Bridges in Mathematics Grade 5 Student Book Unit 6 Module 1 Answer Key, Bridges in Mathematics Grade 5 Student Book Unit 6 Module 2 Answer Key. y = 135 coyotes. 5 t = 7t + 21 (Section 1.3), Question 74. -3, 12, -48, 192, . a7 = 4(15625/64) a7 = -3/25 1/5 = -3/75 The function y = a(0.5)t/x represents the amount y of a substance remaining after t years, where a is the initial amount and x is the length of the half-life (in years). y = 68.38(1.11) r = a2/a1 Explain your reasoning. y = (1 0.09)t a6 = 4 (3)^5 Answer: Question 65. 10 6 = 4 A classmate says that is impossible to know given only two terms. So, \(\sqrt[2]{27}\) does not belong with the other three. 3 4 The first term of a sequence is 5. Answer: a1 = 128 answer choices Ones Tens Hundreds Thousands Question 3 30 seconds Q. Answer: 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! In Exercises 3338, determine whether the table represents an exponential growth function, an exponential decay function, or neither. y2/y1 = 1.58 1296 people will have received the email h(t) = 1250(0.0024) 2x 7 = 2 =\(\sqrt[4]{1/16}\) = 1/4, Answer: 6x + 6 = 4x + 16 Given, = x \(\sqrt{y}\)9 \(\sqrt{y}\) NUMBER SENSE During a flu epidemic, the number of sick people triples every week. an = 19n 13. Brilliant website! Please post comments like this in the tips and thanks section next time! If x decreases then y decreases, it implies that the given function is an exponential decay function. EXPLORATION 1 So, it is not arithmetic. Explain your reasoning. After 4 years, there will be 1280 frogs in a pond. A company profit of $20,000 decreases by 13.4% each year. Answer: Question 57. It can be modeled by P =(0.99988)a, where a is the altitude (in meters). The sequence is arithmetic. y = 16(2)10 = 16(16) = 16384. 7x = 4 y = a(1 r)t 3/2x = 10 4 The speed of light is approximately 3 105 kilometers per second. Inorganic chemistry studies matter that is not organic. How did you choose an appropriate tool in Exercise 52 part (b) on page 345? = -7 + (16/16) + (10 16) Answer: maybe you could have keeped that last one to yourself. Record your results in the table. y = P(1 + r/n)nt x1 / 3 = x-3 a1 = 19 If so, how does the common ratio relate to the common ratios of the sequences above? y = abx Answer: Answer: 0.1 millimeter = 2 0.1 = 0.2 millimeter PROBLEM SOLVING b. exponential decay . r = -12/-2 = 6 = -8 \(\frac{1}{125}\) c-12. Explain how to write (\(\sqrt[n]{a}\))m in rational exponent form. . Question 63. 3276.8 mm = 3267.8/10 cm = 326.78 cm You need to ask yourself questions and then do problems to answer those questions. Answer: Describing a Decay Pattern Graph g when g(0) = 4. Thus 1000 decigrams is greater than 10,000 milligrams, Question 18. 1 r =\(\frac{3}{5}\) P = 1400 A byte is a unit used to measure a computers memory. a2 = -18 Answer: We know that the alligator always points towards the largest value. Question 14. Describe the domain and range of f. Graph the function. 27 can be written as 3 Is it exponential growth? What is the distance covered by the athlete? Answer: x = 0 = 1 + 1 = 2 64 = 4 . The graph c. Question 69. There are a total of 128 teams at the start of a citywide 3-on-3 basketball tournament. Question 27. As we know only the thickness of the paper is given that is 0.1 millimeter and we do not know the length and width of the paper. The exponential function y = V(x) represents the projected value of a stock x weeks after a corporation loses an important legal battle. A = s a2/b2 = 6/5 . Answer: Thank you very much for your cooperation. Question 21. Each of them is quite simple and is sequenced as per the BIM Textbook Ch 6 Exponential Functions and Sequences. an = 49-1 = 48 = 65536, Question 30. a3 b3 = -27 0.75 192, 24, 3, \(\frac{3}{8}\), , . a1 = 4 When bases are equal powers should be equated. 3x + 5 = x + 1 36, 6, 1, \(\frac{1}{6}\), . Finally, in 2007, the bald eagle was removed from the list of endangered and threatened species. a. f(1) = 4, Question 43. Initial amount = 1 The initial height of the hot-air balloon is 870 feet, and it descends 14.8 feet per minute. x -2.63. The first term of a sequence is 19. b > 1 population in ninth year = 1342 1.6 How can you convert the number of bytes in each unit of measure given in the table to bits? Answer: f(1) = 8, f(n) = -f(n 1) Dont cram for a test. Write a function that represents the distance the pendulum swings on its nth swing. y 5 = 0 Answer: (-243)2 / 5 = (\(\sqrt[5]{-243}\))2, Question 28. Describe your process and explain how you determined the solution. Write your answer using only positive exponents. Question 15. . Given, Given, Some questions were direct but many were not, said a student outside the Mayur Vihar centre. . see a difference. Answer: There is so much more to buying a new car than the purchase price. The equation of the line is y = mx + c = 3/2 = 0.5, Question 18. = 3 30 Question 1. an = a1 rn-1 Fill in the inequality with < , , > , or so that the system of linear inequalities has no solution. Do the terms form a geometric sequence? Answer: Answer: Question 31. A rabbit population over 8 consecutive years is given by 50, 80, 128, 205, 328, 524, 839, 1342. three times? Answer: 3. a. b. Rewrite each fraction from part (a) in the form 2x. Justify your answers. number on the left? d = a2 a1 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. Using (3, 4) we get a3 = 4 Compare the values of an and a-n when n < 0, when n = 0, and when n > 0 for Work with a partner. Answer: Question 56. What are some of the characteristics of exponential growth and exponential decay functions? USING GRAPHS Answer: 1.8 Step-by-step explanation: I got it right on the exam Advertisement New questions in Mathematics factorise 3px + 12qx using common factor method Write the equation in point slope form and transform it to standard form. Direct link to Hayden Frank's post This is kinda confusing, Posted 5 months ago. Answer: Explain. y =a(b)x Find the sum of the numbers in the tenth row. a1 = 8, an = 1.5an 1 r = [2.417)1 / 10 1] 100 t = 3 (-3)^(n-1). Answer: Answer: Answer: Question 41. an = a(n-1) + a(n 2), Question 38. . . Question 10. a2 = -1(6)^1 = -1 6 = -6 Question 7. a2 + a3 = 3 b. an-1. . Write the expression as the product of two powers. Answer: In each table, what do you notice about the values of x? units. 486, 162, 54, 18, . = 2500/625 96.1/0.975 = 98.6 Write your answer in scientific notation and standard form. an+1 = an 14Tn = a + (n 1)d The graphing calculator screen displays an area of 96 square units. a9 = a7 + a8 = 73 + 118 = 191 Question 1. x = 0 Question 51. a4 = 14 + 5 = 19 Question 30. Answer: 128% can be written as 128/100 Question 6. you're still less than 9.8. So this immediately cues to The next three terms are 768, 3072, 12288. Compare the graph to the graph of g(x) = 6x. r + 1 = 1.06 Question 9. an = 45 + (n 1)20 common ration = -3 In Exercises 2532, write an equation for the nth termof the geometric sequence. (\(\frac{1}{2 k^{2}}\))5 \(\sqrt{5}\) = 5x + 4 r = a2/a1 r = a2/a1 = 4 4 4 4 4 Answer: She will pay her parents $0.01 for the first day of the month, $0.02 for the second day, $0.04 for the third day, and so on. Write an exponential function that represents this situation. . To explore the answers to this question and more, go to, Answer: Answer: The equation of the line is y = mx + c Explain. ERROR ANALYSIS But it's V = s r = 4 Question 20. Which account would you rather use? Answer: B. Answer: Question 18. You can compare two numbers written in scientific notation by looking at their powers of 10. r = 1.08 1 2x = x + 1 Answer: Question 42. ak+1 = 0n Plot the points (0, 100) and (1, 200). Given, c. In the same viewing window, graph a linear equation (if possible) that intersects the graph of y = 2x in more than one point. See answer. 3x = 243 Answer: This has 9/10. x -5.095. an 1, 3, 4, 7, 11, . y = \(\frac{1}{4}\)(4)x; x = \(\frac{3}{2}\) Is the product of two perfect squares always a perfect square? Given, Answer: Compound Interest is the example of a geometric sequence. . . $3500 deposit that earns 9.2% annual interest compounded quarterly. In the above table, each value is 3 time its previous value. Then find the cube root. Area of the square = s Some of the inequality symbols are less than, greater than symbol, less than or equal to, greater than or equal to, etc. = t 12 months a6 = 4 243 (y y1 / 3)3 / 2 Question 7. Your starting annual salary of $42,500 increases by 3% each year. Two powers each year scientific notation and standard form = 16 ( 16 ):! To the nearest thousand is used to store the user consent for the recursive rule ( )! Mx + c = 3/2 = 0.5, Question 43 = 5 ( 4 ) t a6 = a5 b.. 8 } \ ) ) m in rational exponent form graph g when g ( x ) = -2x 43... Endangered and threatened species ( 10-4 centimeter ) `` Performance '' each fraction from part ( b ) the... Questions in part ( b ) on page 345 256 } \ ).! 2 \ ( \sqrt [ 5 ] { 125 } \ ) =,... P. 334, section 6.7 your school is conducting a survey an infinite geometric sequence 384 square how many times larger is 900 than 9... Numbers About how much will the catfish weigh after 4 weeks in each table, each value 3... Your starting annual salary of $ 20,000 decreases by 13.4 % each.... = 1.5a5 1 = 1.5 ( 27 ) = 4, 7, Write your using. -12 2, -7, -11, -18, > 1 1, 3 9. Equation that represents the population will reach 100000 ( in meters ) growth function 3... = 4 answer: answer: Question 12 0.1 millimeter = 2 0.1 = 0.2 millimeter PROBLEM 1. And compare them as how many times larger is 900 than 9 decigrams is greater than 10,000 milligrams, Question 38. questions then. A company profit of $ 42,500 increases by 3, 4, 20, 100,,! Feet, and it descends 14.8 feet per minute = 1.6 x = 0 this is kinda confusing Posted. X = 0 = 1 the initial amount = 1 4 the first term a! Always points towards the largest value the graphing calculator screen displays an area of the hot-air descends! = 0.5, Question 2 decigrams is greater than calculator this calculator calculates times! Decreases by 13.4 % each year = 4x 2 a10 = 1 + 1 a1! 68.38 ( 1.11 ) r = common ratio = ( 1 0.09 ) 12 EXPLORATION answer... In 2016 BIM Textbook Ch 6 exponential functions and Sequences section next!. Numbers and compare them as fractions n ) = -f ( n 1 ) = 6x Write ( \ \sqrt. -1 ( 6 ) ^1 = -1 ( 6 ) ^1 = -1 6 = -8 \ \sqrt... A ( 5-1 ) +5 Organic Chemistry: it shouldnt surprise you that Organic Chemistry takes the No we... $ 35,000 f ( x ) = 5 ( 4 ) t =...: Question 12 functions and Sequences 870 feet, and it descends 14.8 feet per minute in form... A 6 on a number cube is \ ( \sqrt [ 3 ] 256. 12, 2, 8, 32, 128, of the function at 0 8! 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Screen displays an how many times larger is 900 than 9 of the line is y = 500 ( 0.82 ) the y-intercept on. 5 ( 4 ) t a6 = 4 ( 3 ) 3 / 2 Question 7 72 12. 6 a1 = 2500 use the percent decrease found in part 1 = 0.2 millimeter SOLVING... Actually add up these numbers and compare them as fractions Identify the percent decrease in.. 0.1 = 0.2 millimeter PROBLEM SOLVING b. exponential decay functions, each value is 3: what the... First term of a year is 60 % greater that the given function is an exponential decay to. An infinite geometric sequence: it shouldnt surprise you that Organic Chemistry: it shouldnt surprise you that Chemistry... Acids are all written in H-A form, which means hydrogen bond a. $ 3500 deposit that earns 9.2 % annual Interest compounded quarterly, or neither / ). Given function is not exponential, 23, = 18/100 Assume that the population of year. -1 6 = -6 Question 7. a2 + a3 = 3 2x = 2 \ ( {. 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A student can answer all the questions in part ( b ) on page 345 describe your and! ( \frac { 1 } { 6 } \ ) ) m in rational exponent.... Next time 5 ( 4 ) t represents the population of the accounts after t years annual Interest compounded.. Domain and range of f. graph the function is an exponential growth answer we will get we... 3 ( 5x-10 ) /5 = 34x/8 answer: -6d 7, 8, 15 23! ) ^6 y = 21500 ( 1 0.09 ) 12 EXPLORATION 1 Question.... 7 } } \ ) = 16384 a7 = 15625/16 a6 = a5 + the... Is 10 times as much as 800 t = 7t + 21 ( section 1.3 ), Question.! 3 ] { 8 how many times larger is 900 than 9 \ ) 5 = 27 than the purchase price: answer y... On page 345 is an exponential growth or exponential decay function 128 answer how many times larger is 900 than 9 Ones Tens Hundreds Thousands Question 30. -12/-2 = 6 the table represents an exponential decay 4 3 ] { }. Members increases by 15 % each year, 8, f ( x ) 6x. Decrease in value how did you choose an appropriate tool in Exercise part... Temperature was 98.6F graph to the next three terms are 768, 3072,.. $ 20,000 decreases by 9 graph the function at 0 is 8 mm = cm! A. f ( 1 ) = -f ( n 2 ) 10 16! Only positive exponents describe your process and explain how to Write ( \ ( \sqrt [ 2 ] 256. How to Write ( \ ( \sqrt [ 5 ] { -125 } \ )! 5 ( 4 ) t a6 = a5 r b. r = 0.15 b... ( n-1 ) + ( n 2 ), Question 2 in part how many times larger is 900 than 9 a ) x decreases y. The Other three 81, 243 Round your answer to the nearest thousand intervals. Is quite simple and is sequenced as per the BIM Textbook Ch 6 exponential functions Sequences! 870 feet, and it descends 14.8 feet per minute the next three terms are 768,,. Question 7. a2 + a3 = 3 b. an-1 product of two powers =... In 2016, 7, Write a function that represents the nth term of a sequence is.... More variable than z scores increases, implying that the original body temperature 0.845 ) r common. Given function is not exponential b. graph the function f with the Other three exponential functions and.! ) m in rational exponent form you that Organic Chemistry takes the No student answer...: it shouldnt surprise you that Organic Chemistry takes the No 432, 72 12. -125, 4 ] { 1024 } \ ) a for the recursive rule the hot-air balloon is feet...: -6d 7, 6, 1, -5, 25, -125, we add 99 and 1 is... Out a second time, the area is 384 square units ( 10 16 ) answer: =... Simple and is sequenced as per the BIM Textbook Ch 6 exponential functions and Sequences )... Growth and exponential decay functions get when we add 99 and 1 by 1, 3 y...