Name: Class: Date: 6. What is the y intercept of the function h(x) = 3 x 3 a. (0, -2) b. (-2, 0) c. (-3, 0) d. (0, -3)

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1 Name: Class: Date: ID: A Exponential Study Guide 1. Identify each of the following for the function f(x) = 4 2 x. Then graph the function. a. x-intercept(s) b.y-intercept c. asymptote d. domain e. range f. interval(s)of increase/decrease 2. What is the classification of the function f(x) = 5 x 1? 6. What is the y intercept of the function h(x) = 3 x 3 a. (0, -2) b. (-2, 0) c. (-3, 0) d. (0, -3) 7. Write an exponential function for the graph. a. linear absolute value function b. exponential function c. quadratic function d. linear function 3. Determine if the sequence 184, 207, 230, 253, is arithmetic or geometric. Then identify the next term in the sequence. a. arithmetic; 23 b. arithmetic; 276 c. geometric; 23 d. geometric; Kathy plans to purchase a car that depreciates (loses value) at a rate of 14% per year. The initial cost of the car is $21,000. Which equation represents the value, v, of the car after 3 years? a. v = 21,000(0.14) 3 b. v = 21,000(0.86) 3 c. v = 21,000(1.14) 3 d. v = 21,000(0.86)(3) 5. What is the solution to the exponential equation 1 64 = 2x + 1? a. x = 7 b. x = 6 c. x = 5 d. x = 5 a. y = 0.5(2) x b. y = 2(0.5) x c. y = (2 0.5) x d. y = 2(5) x 8. Find the value of $1000 deposited for 10 years in an account paying 7% annual interest compounded yearly. Represent each reflection using coordinate notation. Identify whether g(x) is a reflection about a horizontal line of reflection or a vertical line of reflection. 9. f(x) = 2 x g(x) = (2 x ) 10. f(x) = 2 x g(x) = 2 x 1

2 Name: ID: A 11. What is the y-intercept of the function f(x) = 0.4 x + 2? 12. Which shows the function f(x) = 7x after a vertical translation 4 units down? a. g(x) = 7x + 4 b. g(x) = 7x 4 c. g(x) = 4x + 7 d. g(x) = 4x Which shows the function f(x) = 2x 4 after a horizontal translation 2 units left? a. f(x) = 2x b. f(x) = 2x 4 2 c. f(x) = 2(x + 2) 4 d. f(x) = 2(x 2) What is the equation for the line that represents the horizontal asymptote of the function f(t) = 25,000( ) x? 15. a. x = 0 b. y = 0 c. x = 25,000 d. y = 25,000 Determine whether the data in the table display exponential behavior. Explain why or why not. x y a. No; the domain values are at regular intervals. b. No; a different value is added to each range value. c. No; there is no relationship between the x value and its corresponding y value. d. Yes; the domain values are at regular intervals and the range values have a common factor Given the explicit formula for a geometric sequence find the recursive formula. 17. Determine the 7th term in the sequence defined by n 1 Ê 1ˆ g n = 2. Á Daniel s Print Shop purchased a new printer for $35,000. Each year it depreciates (loses value) at a rate of 5%. What will its approximate value be at the end of the fourth year? a. $33, b. $30, c. $28, d. $27, The population of Henderson City was 3,381,000 in 1994, and is growing at an annual rate of 1.8%. If this growth rate continues, what will the approximate population of Henderson City be in the year 2000? a. 3,696,000 b. 3,763,000 c. 3,798,000 d. 3,831, Find the annual percent increase or decrease that y = 0.35(2.3) x models. a. 230% increase b. 130% increase c. 30% decrease d. 65% decrease 21. Given the explicit formula for a geometric sequence find the first five terms and the term named in the problem. 2

3 Name: ID: A Tell whether the graph represents exponential growth or exponential decay. Then write a rule for the function The New York Volleyball Association invited 64 teams to compete in a tournament. After each round, half of the teams were eliminated. Which equation represents the number of teams, t, that remained in the tournament after r rounds? a. t = 64(r) 0.5 b. t = 64( 0.5) r c. t = 64(1.5) r d. t = 64(0.5) r 26. The enrollment at Alpha-Beta School District has been declining 3% each year from 1994 to If the enrollment in 1994 was 2583, find the 2000 enrollment. Ê 27. What is the range of the function f(x) = 2 ˆ Á 3 x + 2? 3

4 Name: ID: A 28. Find the average rate of change over the interval 29. Determine if the sequence is arithmetic or geometric. Then identify the next term in the sequence. 0.2, 1, 5, 25, a. arithmetic; 75 b. arithmetic; 125 c. geometric; 75 d. geometric; Shelby s printer had 500 sheets of paper in it. After Monday, there were 466 sheets of paper. After Tuesday, there were 432 sheets of paper. After Wednesday, there were 398 sheets of paper. If this pattern continues, how many sheets of paper will be left after Friday? a. 34 b. 296 c. 330 d Explain the difference between a linear function and an exponential function when the functions are represented in the following ways. a. by equations b. by graphs c. by tables 32. For each sequence, write a recursive formula. a. 2 5, 6 5, 18 5, 54 5, b. 25, 12, 1, 14, 27 c. 1, 11, 121, 1,331, 14,641 d. 3.14, 3.37, 3.6, 3.83, The Booster Club raised $30,000 for a sports fund. No more money will be placed into the fund. Each year the fund will decrease by 5%. Determine the amount of money, to the nearest cent, that will be left in the sports fund after 4 years. 4

5 Name: ID: A Ê 4x 3 ˆ Á 34. The expression 2x a. 4x 4 b. 4x 5 c. 8x 4 d. 8x 5 2 is equivalent to 35. The profit for a company this year was $100,000. Each year the profit increases at a rate of 1.2% per year. Which function shows the company s profit as a function of time in years? a. f(t) = 100, t b. f(t) = 100,000( ) t c. f(t) = 100,000( ) t d. f(t) = 100, t 36. You drop a ball from a height of 0.5 meter. Each curved path has 52% of the height of the previous path. a. Write a rule for the sequence using centimeters. The initial height is given by the term n = 1. b. What height will the ball be at the top of the third path? a. A(n) = 50 (52) n 1 ; 135,200 cm b. A(n) = 0.5 (0.52) n 1 ; 0.14 cm c. A(n) = 50 (0.52) n 1 ; cm d. A(n) = 0.52 (0.5) n 1 ; 0.13 cm 37. On January 1, 1999, the price of gasoline was $1.39 per gallon. If the price of gasoline increased by 0.5% per month, what was the cost of one gallon of gasoline, to the nearest cent, on January 1 one year later? 38. Write an exponential function to model the situation. Then estimate the value of the function after 5 years (to the nearest whole number). A population of 290 animals that increases at an annual rate of 9%. 39. Write a rule for the function. x y For each sequence, write an explicit formula. a. 1 6, 5 6, 3 2, 13 6, 17 6 b. 1, 10, 100, 1,000, 10,000 c. 96, 48, 24, 12, 6 d. 10.2, 2.2, 5.8, 13.8, 21.8 Ê 41. What is the range of the function f(x) = 1 ˆ Á 4 a. x < 0 b. x > 0 c. f(x) < 0 d. f(x) > 0 x? 42. Write a rule for the function. x y

6 Name: ID: A 43. Find the y-intercept of the equation. f(x) = 4( 3) x a. 4 b. -12 c. 3 d Suppose the population of a town is 2,700 and is growing 4% each year. a. Write an equation to model the population growth. b. Predict the population after 12 years. a. y = 4 2, 700 x ; about 129,600 people b. y = 2, x ; about 4,323 people c. y = 2, x ; about 4,323 people d. y = 2, x ; about 45,298,483,200 people 45. In a science fiction novel, the main character found a mysterious rock that decreased in size each day. The table below shows the part of the rock that remained at noon on successive days. 46. Nintendo brand s value decreased by 11.2% from 2002 to Assume this continues. If the company had a value of $9,220,000 in 2002, write an equation for the value of Nintendo for t years after a. y = 9,220,000( 0.112) t b. y = 9,220,000( t) c. y = 9,220,000( 1.112) t.112 d. y = 9,220,000( ) t 47. Identify each of the following for the function y = 1 x Ê ˆ. Á 3 a. x-intercept(s) b. y-intercept c. asymptote d. domain e. range f. interval(s) of increase/decrease Which fractional part of the rock will remain at noon on day 7? a b c d Raymond is filling his kitchen sink to wash dishes. After one minute, there are 2.75 gallons of water in the sink. After two minutes, there are 5.5 gallons of water in the sink. After three minutes, there are 8.25 gallons of water in the sink. If this pattern continues, how many gallons of water will be in the sink after five minutes? a b. 11 c d

7 Name: ID: A 49. Which explicit formula is represented by the graph? 51. A radioactive substance has an initial mass of 100 grams and its mass halves every 4 years. Which expression shows the number of grams remaining after t years? a. 100(4) t 4 b. 100(4) 2t Ê c ˆ Á 2 Ê d ˆ Á 2 t 4 4t 52. What is the solution to the exponential equation 81 = 3 x 1? a. g n = 1 n 1 b. g n = ( 1) n 1 c. g n = 2 n 1 d. g n = ( 2) n Brittany is a scientist. She is recording the number of cells in a dish. After each hour, the cell divides into four cells. The sequence shown represents the growth of the cells. 1, 4, 16, 64, 256, Which explicit formula represents this situation? a. g n = 4 n 1 b. g n = 4 1 n 1 c. g n = 4 n 1 d. g n = 4 1 n 1 a. x = 3 b. x = 3 c. x = 4 d. x = Write an exponential function to model the situation. A population of 470 animals decreases at an annual rate of 12%. a. y = 470( 1.88) x b. y = 470( 1.12) x c. y = 470( 0.12) x d. y = 470( 0.88) x Write a rule for the nth term of the geometric sequence. 54. a 1 = 4 and r = 1 2 7

8 Exponential Study Guide Answer Section 1. ANS: a. none b. (0, 4) c. f(x) = 0 d. all real numbers e. f(x) < 0 f. decreasing over the entire domain PTS: 1 REF: 5.2 NAT: A.SSE.1.a A.SSE.1.b A.CED.1 A.REI.11 F.IF.4 F.IF.7.e F.LE.5 F.LE.2 STA: A.SSE.1.a A.SSE.1.b A.CED.1 A.REI.11 F.IF.4 F.IF.7.e F.LE.5 F.LE.2 TOP: Post Test KEY: horizontal asymptote 2. ANS: B PTS: 1 REF: 1.3 NAT: F.IF.5 F.IF.9 A.REI.10 F.IF.1 F.IF.2 F.IF.7.a STA: F.IF.5 F.IF.9 A.REI.10 F.IF.1 F.IF.2 F.IF.7.a TOP: Standardized Test KEY: function notation increasing function decreasing function constant function function family linear functions exponential functions absolute minimum absolute maximum quadratic functions linear absolute value functions linear piecewise functions 3. ANS: B PTS: 1 REF: 4.3 NAT: F.BF.1.a F.BF.2 A.SSE.1.a F.LE.1.b F.LE.1.c F.LE.2 STA: F.BF.1.a F.BF.2 A.SSE.1.a F.LE.1.b F.LE.1.c F.LE.2 TOP: Standardized Test KEY: index explicit formula recursive formula 4. ANS: B PTS: 2 REF: ia TOP: Exponential Functions 1

9 5. ANS: A PTS: 1 REF: 5.6 NAT: A.REI.3 A.CED.1 A.CED.2 N.Q.2 A.REI.10 A.REI.11 N.RN.2 F.LE.2 STA: A.REI.3 A.CED.1 A.CED.2 N.Q.2 A.REI.10 A.REI.11 N.RN.2 F.LE.2 TOP: Standardized Test 6. ANS: D PTS: 1 7. ANS: A PTS: 1 DIF: L2 REF: 8-1 Exploring Exponential Models OBJ: Exponential Growth NAT: NAEP A2h CAT5.LV21/22.50 CAT5.LV21/22.53 IT.LV17/18.AM IT.LV17/18.DI IT.LV17/18.PS S9.TSK3.DSP S9.TSK3.PRA S10.TSK3.DSP S10.TSK3.PRA TV.LV21/22.15 TV.LV21/22.17 TV.LV21/22.52 TV.LVALG.53 TV.LVALG.56 TOP: 8-1 Example 3 KEY: exponential function graphing growth factor MSC: NAEP A2h CAT5.LV21/22.50 CAT5.LV21/22.53 IT.LV17/18.AM IT.LV17/18.DI IT.LV17/18.PS S9.TSK3.DSP S9.TSK3.PRA S10.TSK3.DSP S10.TSK3.PRA TV.LV21/22.15 TV.LV21/22.17 TV.LV21/22.52 TV.LVALG.53 TV.LVALG ANS: $ PTS: 1 DIF: Level B REF: MAL21013 TOP: Lesson 8.5 Write and Graph Exponential Growth Functions KEY: compound interest MSC: Application NOT: ANS: (x, y) (x, y) g(x) is a horizontal reflection about y = 0. PTS: 1 REF: 5.4 NAT: F.IF.4 A.REI.10 F.LE.2 STA: F.IF.4 A.REI.10 F.LE.2 TOP: Skills Practice KEY: reflection line of reflection 10. ANS: (x, y) ( x, y) g(x) is a vertical reflection about x = 0. PTS: 1 REF: 5.4 NAT: F.IF.4 A.REI.10 F.LE.2 STA: F.IF.4 A.REI.10 F.LE.2 TOP: Skills Practice KEY: reflection line of reflection 11. ANS: (0, 2) PTS: 1 REF: 5.2 NAT: A.SSE.1.a A.SSE.1.b A.CED.1 A.REI.11 F.IF.4 F.IF.7.e F.LE.5 F.LE.2 STA: A.SSE.1.a A.SSE.1.b A.CED.1 A.REI.11 F.IF.4 F.IF.7.e F.LE.5 F.LE.2 TOP: Mid Ch Test KEY: horizontal asymptote 12. ANS: B PTS: 1 REF: 5.3 NAT: F.BF.3 A.REI.10 F.LE.2 STA: F.BF.3 A.REI.10 F.LE.2 TOP: Standardized Test KEY: basic function transformation vertical translation coordinate notation horizontal translation argument of a function 2

10 13. ANS: C PTS: 1 REF: 5.3 NAT: F.BF.3 A.REI.10 F.LE.2 STA: F.BF.3 A.REI.10 F.LE.2 TOP: Standardized Test KEY: basic function transformation vertical translation coordinate notation horizontal translation argument of a function 14. ANS: B PTS: 1 REF: 5.2 NAT: A.SSE.1.a A.SSE.1.b A.CED.1 A.REI.11 F.IF.4 F.IF.7.e F.LE.5 F.LE.2 STA: A.SSE.1.a A.SSE.1.b A.CED.1 A.REI.11 F.IF.4 F.IF.7.e F.LE.5 F.LE.2 TOP: Standardized Test KEY: horizontal asymptote 15. ANS: D If the domain values are at regular intervals and the range values have a common factor, the data are probably exponential. A B C D Feedback If the domain values are at regular intervals and the range values have a common factor, the data are probably exponential. What can you multiply each range value by to get the next value? If the domain values are at regular intervals and the range values have a common factor, the data are probably exponential. Correct! PTS: 1 DIF: Basic OBJ: Identify data that displays exponential behavior. NAT: NA 2 NA 8 NA 9 NA 10 NA 6 TOP: Identify data that displays exponential behavior KEY: Exponential Functions Identify Graphs 16. ANS: PTS: ANS: Ê 1ˆ g 1 = 2 Á 2 6 Ê 1ˆ g 1 = 2 Á 2 Ê 1 ˆ g 1 = 2 Á 64 g 1 = PTS: 1 REF: 4.3 NAT: F.BF.1.a F.BF.2 A.SSE.1.a F.LE.1.b F.LE.1.c F.LE.2 STA: F.BF.1.a F.BF.2 A.SSE.1.a F.LE.1.b F.LE.1.c F.LE.2 TOP: End Ch Test KEY: index explicit formula recursive formula 3

11 18. ANS: C 35000(1 0.05) PTS: 2 REF: fall0719ia TOP: Exponential Functions 19. ANS: B PTS: 2 REF: fall9916b TOP: Exponential Functions 20. ANS: B PTS: 1 DIF: L3 REF: 8-1 Exploring Exponential Models OBJ: Exponential Decay NAT: NAEP A2h CAT5.LV21/22.50 CAT5.LV21/22.53 IT.LV17/18.AM IT.LV17/18.DI IT.LV17/18.PS S9.TSK3.DSP S9.TSK3.PRA S10.TSK3.DSP S10.TSK3.PRA TV.LV21/22.15 TV.LV21/22.17 TV.LV21/22.52 TV.LVALG.53 TV.LVALG.56 TOP: 8-1 Example 6 KEY: exponential decay exponential function exponential growth percent MSC: NAEP A2h CAT5.LV21/22.50 CAT5.LV21/22.53 IT.LV17/18.AM IT.LV17/18.DI IT.LV17/18.PS S9.TSK3.DSP S9.TSK3.PRA S10.TSK3.DSP S10.TSK3.PRA TV.LV21/22.15 TV.LV21/22.17 TV.LV21/22.52 TV.LVALG.53 TV.LVALG ANS: PTS: ANS: Exponential growth; y = 5 2 x PTS: 1 DIF: Level B REF: 7ef77408-cdbb-11db-b f7 TOP: Lesson 8.6 Write and Graph Exponential Decay Functions KEY: Exponential growth exponential decay MSC: Knowledge NOT: ANS: x Ê Exponential decay; y = 2 3 x 1ˆ or y = 2 Á 3 PTS: 1 DIF: Level B REF: 7ef66203-cdbb-11db-b f7 TOP: Lesson 8.6 Write and Graph Exponential Decay Functions KEY: Exponential growth exponential decay MSC: Knowledge NOT:

12 24. ANS: PTS: ANS: D PTS: 2 REF: ia TOP: Exponential Functions 26. ANS: 2152 PTS: 1 DIF: Level B REF: MALG1215 TOP: Lesson 8.6 Write and Graph Exponential Decay Functions KEY: write solve word exponential equation MSC: Comprehension NOT: ANS: f(x) > 2 PTS: 1 REF: 5.2 NAT: A.SSE.1.a A.SSE.1.b A.CED.1 A.REI.11 F.IF.4 F.IF.7.e F.LE.5 F.LE.2 STA: A.SSE.1.a A.SSE.1.b A.CED.1 A.REI.11 F.IF.4 F.IF.7.e F.LE.5 F.LE.2 TOP: Mid Ch Test KEY: horizontal asymptote 28. ANS: d) -7/3 e) 3/2 PTS: ANS: D PTS: 1 REF: 4.3 NAT: F.BF.1.a F.BF.2 A.SSE.1.a F.LE.1.b F.LE.1.c F.LE.2 STA: F.BF.1.a F.BF.2 A.SSE.1.a F.LE.1.b F.LE.1.c F.LE.2 TOP: Standardized Test KEY: index explicit formula recursive formula 30. ANS: C PTS: 1 REF: 4.1 NAT: F.LE.1.b F.LE.1.c F.LE.2 STA: F.LE.1.b F.LE.1.c F.LE.2 TOP: Standardized Test KEY: sequence term of a sequence infinite sequence finite sequence 5

13 31. ANS: a. A linear function can be written in the form y = ax + b. An exponential function is written in the form y = ab x. b. The graph of a linear function is a straight line. The graph of an exponential function is a curve. c. In a linear function, the differences between the corresponding y-values of consecutive x-values are the same. In an exponential function, the quotients of the corresponding y-values of consecutive x-values are the same. PTS: 1 DIF: Level B REF: MAL21026 NAT: NCTM 9-12.ALG.1.e TOP: Lesson 8.5 Write and Graph Exponential Growth Functions KEY: exponential function linear MSC: Analysis NOT: ANS: a. g n = g n 1 3 b. a n = a n c. g n = g n 1 ( 11) d. a n = a n PTS: 1 REF: 4.3 NAT: F.BF.1.a F.BF.2 A.SSE.1.a F.LE.1.b F.LE.1.c F.LE.2 STA: F.BF.1.a F.BF.2 A.SSE.1.a F.LE.1.b F.LE.1.c F.LE.2 TOP: End Ch Test KEY: index explicit formula recursive formula 33. ANS: 24, (.95) PTS: 4 REF: ia TOP: Exponential Functions 34. ANS: D Ê Á 4x 3 ˆ 2 = 16x 6 2x 2x = 8x 5 PTS: 2 REF: ia TOP: Powers of Powers 35. ANS: C PTS: 1 REF: 5.1 NAT: A.SSE.1.a A.SSE.1.b A.CED.1 F.IF.3 F.IF.6 F.IF.7.e F.BF.1.a F.BF.2 F.LE.1.a F.LE.1.b F.LE.1.c F.LE.2 F.LE.3 F.LE.5 STA: A.SSE.1.a A.SSE.1.b A.CED.1 F.IF.3 F.IF.6 F.IF.7.e F.BF.1.a F.BF.2 F.LE.1.a F.LE.1.b F.LE.1.c F.LE.2 F.LE.3 F.LE.5 TOP: Standardized Test KEY: simple interest compound interest 36. ANS: C PTS: 1 DIF: L2 REF: 8-6 Geometric Sequences OBJ: Using a Formula NAT: NAEP A1a NAEP A1i CAT5.LV19.47 CAT5.LV19.52 CAT5.LV19.54 IT.LV15.CP IT.LV15.DI IT.LV15.I S9.TSK1.NS S10.TSK1.NS TV.LV19.10 TV.LV19.16 TV.LV19.17 TV.LV19.52 TV.LVALG.53 TOP: 8-6 Example 5 KEY: geometric sequence problem solving word problem multi-part question MSC: NAEP A1a NAEP A1i CAT5.LV19.47 CAT5.LV19.52 CAT5.LV19.54 IT.LV15.CP IT.LV15.DI IT.LV15.I S9.TSK1.NS S10.TSK1.NS TV.LV19.10 TV.LV19.16 TV.LV19.17 TV.LV19.52 TV.LVALG.53 6

14 37. ANS: PTS: 2 REF: b TOP: Exponential Functions 38. ANS: f(x) = 290( 1.09) x ; 446 PTS: 1 DIF: Level B REF: MAL21010 TOP: Lesson 8.5 Write and Graph Exponential Growth Functions KEY: exponential growth decay write equation word MSC: Application NOT: ANS: A rule for the function is y = x PTS: 1 DIF: Level B REF: A FR.07 NAT: NCTM 9-12.ALG.1.a NCTM 9-12.ALG.1.b NCTM 9-12.ALG.1.c NCTM 9-12.ALG.2.c STA: GA MM1A1.f GA.GPS.MTH.04.MA1.MM1A1.f TOP: Lesson 8.5 Write and Graph Exponential Growth Functions KEY: free response function exponential MSC: Comprehension NOT: ANS: a. a n = (n 1) 3 b. g n = 1 ( 10) n 1 c. g n = 96 (0.5) n 1 d. a n = (n 1) PTS: 1 REF: 4.3 NAT: F.BF.1.a F.BF.2 A.SSE.1.a F.LE.1.b F.LE.1.c F.LE.2 STA: F.BF.1.a F.BF.2 A.SSE.1.a F.LE.1.b F.LE.1.c F.LE.2 TOP: End Ch Test KEY: index explicit formula recursive formula 41. ANS: D PTS: 1 REF: 5.2 NAT: A.SSE.1.a A.SSE.1.b A.CED.1 A.REI.11 F.IF.4 F.IF.7.e F.LE.5 F.LE.2 STA: A.SSE.1.a A.SSE.1.b A.CED.1 A.REI.11 F.IF.4 F.IF.7.e F.LE.5 F.LE.2 TOP: Standardized Test KEY: horizontal asymptote 7

15 42. ANS: A rule for the function is y = x PTS: 1 DIF: Level B REF: A FR.07 STA: GA.GPS.MTH.04.MA1.MM1A1.f GA.GPS.MTH.04.MA3.MM3A2.g TOP: Lesson 8.5 Write and Graph Exponential Growth Functions KEY: free response function exponential MSC: Comprehension NOT: ANS: A PTS: 1 DIF: Level B REF: MAL21004 STA: GA.GPS.MTH.04.MA1.MM1A1.d GA.GPS.MTH.04.MA2.MM2A2.b GA.GPS.MTH.04.MA3.MM3A2.e TOP: Lesson 7.1 Graph Exponential Growth Functions KEY: exponential equation MSC: Knowledge NOT: ANS: C PTS: 1 DIF: L1 REF: Growing Growing Growing Skills Practice Investigation 3 OBJ: Investigation 3: Growth Factors and Growth Rates NAT: NAEP A1a NAEP A1b NAEP A1e NAEP A2g STA: 8GA M8P4.a 8GA M8P4.c TOP: Problem 3.2 Growth Rates Problem 3.3 Connecting Growth Rates and Growth Factor KEY: exponential growth growth factor problem solving word problem multi-part question MSC: NAEP A2h CAT5.LV19.50 CAT5.LV19.54 IT.LV15.PS IT.LV15.AM S9.TSK1.NS S10.TSK1.NS TV.LV19.18 TV.LV19.52 TV.LVALG ANS: B R = 0.5 d 1 PTS: 2 REF: ia TOP: Exponential Functions 46. ANS: D The equation for exponential decay is y = C( 1 r), where y represents the final amount, C represents the initial amount, r represents the rate of change expressed as a decimal, and t represents time. y = 9,220,000( ) Feedback A Don't forget to add subtract the rate of change from 1. B Raise what is in the parentheses to the t power. C The initial amount is multiplied by 1 minus the rate of change to the t power. D Correct! PTS: 1 DIF: Basic OBJ: Solve problems involving exponential decay. NAT: NA 2 NA 8 NA 9 NA 10 NA 6 TOP: Solve problems involving exponential decay KEY: Exponential Decay Solve Problems 8

16 47. ANS: a. x-intercept(s) b.y-intercept c. asymptote d. domain e. range f. interval(s)of increase/decrease PTS: 1 REF: 5.2 NAT: A.SSE.1.a A.SSE.1.b A.CED.1 A.REI.11 F.IF.4 F.IF.7.e F.LE.5 F.LE.2 STA: A.SSE.1.a A.SSE.1.b A.CED.1 A.REI.11 F.IF.4 F.IF.7.e F.LE.5 F.LE.2 TOP: End Ch Test KEY: horizontal asymptote 48. ANS: C PTS: 1 REF: 4.1 NAT: F.LE.1.b F.LE.1.c F.LE.2 STA: F.LE.1.b F.LE.1.c F.LE.2 TOP: Standardized Test KEY: sequence term of a sequence infinite sequence finite sequence 49. ANS: C PTS: 1 REF: 4.4 NAT: F.IF.1 F.IF.4 F.LE.2 STA: F.IF.1 F.IF.4 F.LE.2 TOP: Standardized Test 50. ANS: A PTS: 1 REF: 4.3 NAT: F.BF.1.a F.BF.2 A.SSE.1.a F.LE.1.b F.LE.1.c F.LE.2 STA: F.BF.1.a F.BF.2 A.SSE.1.a F.LE.1.b F.LE.1.c F.LE.2 TOP: Standardized Test KEY: index explicit formula recursive formula 51. ANS: C PTS: 2 REF: b TOP: Exponential Functions 52. ANS: D PTS: 1 REF: 5.6 NAT: A.REI.3 A.CED.1 A.CED.2 N.Q.2 A.REI.10 A.REI.11 N.RN.2 F.LE.2 STA: A.REI.3 A.CED.1 A.CED.2 N.Q.2 A.REI.10 A.REI.11 N.RN.2 F.LE.2 TOP: Standardized Test 53. ANS: D PTS: 1 DIF: Level B REF: MALG1214 STA: GA.GPS.MTH.04.MA2.MM2A2.e GA.GPS.MTH.04.MA3.MM3A2.g TOP: Lesson 8.6 Write and Graph Exponential Decay Functions KEY: equation exponential growth decay write MSC: Knowledge NOT: ANS: a n = 4 1 n 1 Ê ˆ Á 2 PTS: 1 DIF: Level B REF: MAL21625 NAT: NCTM 9-12.ALG.1.a STA: GA.GPS.MTH.04.MA1.MM1A1.f TOP: Lesson 12.3 Analyze Geometric Sequences and Series KEY: geometric sequence MSC: Knowledge NOT: