Algebra Exponentials Jeopardy Algebra Exponentials Jeopardy graphs properties

Algebra Exponentials Jeopardy

Algebra Exponentials Jeopardy graphs properties mystery 1 1 1 2 2 2 3 3 3 4 4 4 Final Jeopardy interest applications other 1 2 3 4

Graphing 1 point A. Growth or decay? B. X-intercept C. Y-intercept

Graphing 1 point answer A. Growth B. No x-intercept for exponential functions! C. (0, 1)

Graphing 2 points A. Growth or decay B. X-intercept C. Y-intercept

Graphing 2 points answer A. Decay B. No x-intercepts for exponentials! C. (0, 4)

Graphing 3 points A. B. C. D. E. F. Growth or decay X-intercept Y-intercept Domain Range asymptote

Graphing 3 points answer •

Graphing 4 points A. Growth or decay B. Write the rule C. Domain D. Range E. Asymptote (0, 6) and (2, 0. 375)

Graphing 4 points answer •

Properties 1 point 2 0 (-4 xy )

Properties 1 point answer 2 0 (-4 xy ) 1

Properties 2 points 4 -3 -5 8 2 b ⋅ 4 a ⋅ 5 b ⋅ -2 a

Properties 2 points answer •

Properties 3 points Rewrite with only one exponent: 3 6 12 64 x y z

Properties 3 points answer 64 x 3 y 6 z 12 These can all be written to the power of 3: 43 x 3(y 2)3(z 4)3 2 4 3 (4 xy z )

Properties 4 points Solve: 6 x 20 5 = 125

Properties 4 points answer 6 x 20 5 = 125 Rewrite 125 with a base of 5 56 x = (53)20 56 x = 560 6 x = 60 X = 10

Mystery 1 point •

Mystery 1 point answer •

Mystery 2 points •

Mystery 2 points answer •

Mystery 3 points State the: Domain Range Y-intercept X-intercept

Mystery 3 points answer •

Mystery 4 points You have two neighbors with dogs. The first neighbor will give you $7 each time you walk his dog. The second neighbor will give you $. 50 for the first walk, then doubles each walk after that. A. How much total will each neighbor have given you after 4 walks? B. When will it be better for you to choose the second neighbor?

Mystery 4 points answer A. Neighbor #1: $7(4) = $28 Neighbor #2: $0. 50 + $1 + $2 + $4 = $7. 50 B. On walk 7 your first neighbor will have given you $49 and the second neighbor will have paid you a total of $63. 50

Interest 1 point Invest $850 in an account that pays 2% interest compounded annually for 4 years.

Interest 1 point answer Invest $850 in an account that pays 2% interest compounded annually for 4 years. P = 850 R = 2%/1 = 2% + 100% = 102% = 1. 02 X = 4(1) A = 850(1. 02)4 = $920. 07

Interest 2 points Invest $9000 in an account that pays 3% interest compounded semiannually for 6 years.

Interest 2 points answer Invest $9000 in an account that pays 3% interest compounded semiannually for 6 years. P = 9000 R = 3%/2 = 1. 5% + 100% = 101. 5% = 1. 015 X = 6(2) = 12 A = 9000(1. 015)12 = $10, 760. 56

Interest 3 points Invest $1000 in an account that pays 5% compounded quarterly for 10 years.

Interest 3 points answer Invest $1000 in an account that pays 5% compounded quarterly for 10 years. P = 1000 R = 5%/4 = 1. 25% + 100% = 101. 25% = 1. 0125 X = 10(4) = 40 A = 1000(1. 0125)40 = $1643. 62

Interest 4 points Invest $12, 000 in an account that pays 3% compounded monthly for 8 years.

Interest 4 points answer Invest $12, 000 in an account that pays 3% compounded monthly for 8 years. P = 12000 R = 3%/12 = 0. 25% + 100% = 100. 25% = 1. 0025 X = 8(12) = 96 A = 12000(1. 0025)96 = $15, 250. 42

Applications 1 point A club has 20 people and is growing by 15% each year. How many members will there be in 6 years?

Applications 1 point answer A club has 20 people and is growing by 15% each year. How many members will there be in 6 years? a = 20 b = 15% + 100% = 115% = 1. 15 x = 6 Y = 20(1. 15)6 = 46 people

Applications 2 points A car depreciates by 13% each year. How much will a car currently valued at $21, 000 be worth in 7 years?

Applications 2 points answer A car depreciates by 13% each year. How much will a car currently valued at $21, 000 be worth in 7 years? a = 21000 b = 100% - 13% = 87% = 0. 87 x = 7 y = 21000(0. 87)7 = $7922. 35

Applications 3 points A haunted house has 5 spiders. Their population is doubling every 4 months. How many spiders will there be in 10 years?

Applications 3 points answer A haunted house has 5 spiders. Their population is doubling every 4 months. How many spiders will there be in 10 years? a=5 b = 2 (doubling = 2) x = 3 times a year for 10 years = 30 5(2)30 = 5, 368, 709, 120

Applications 4 points A mystery substance has a half life of 2 days. If you start with 17 mg of this substance, how much will be left in 13 days?

Applications 4 points answer A mystery substance has a half life of 2 days. If you start with 17 mg of this substance, how much will be left in 13 days? a = 17 mg b = 0. 5 (half life is ALWAYS 0. 5) x = 13/2 = 6. 5 cycles y = 17(0. 5)6. 5 = 0. 19 mg

Other 1 point A. B. C. D. y = 0. 5(1. 25)x Growth or decay? Y-intercept Rate of growth or decay Growth or decay factor

Other 1 point answer y = 0. 5(1. 25)x A. Growth or decay? Growth (b > 1) B. Y-intercept (also known as “a” 0. 5) C. Rate of growth or decay b = 1. 25, growing by 25% D. Growth factor: 1. 25

Other 2 points 5 3 2 (-4 xy z )

Other 2 points answer 5 3 2 (-4 xy z ) = 2 10 6 16 x y z

Other 3 points Graph y = -2(0. 5)x What are the domain and range?

other 3 points answer •

Other 4 points You buy a brand new car for $35000. It loses its value by 9% each year. A. Write an equation to model this situation. B. What is the domain? C. What is the range?

Other 4 points answer •

Final Jeopardy Write a rule to model the data. x y 1 10 2 12. 5 3 4 15. 625 19. 531

Final Jeopardy answer Write a rule: y = a(b)x 10 = a(1. 25) a = 10/1. 25 = 8 12. 5 = a(b)2 10 = a(b)1 1. 25 = b 1 y = 8(1. 25)x