Algebra Exponentials Jeopardy

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

Graphing 1 point Growth or decay? X-intercept Y-intercept

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

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

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

Graphing 3 points Growth or decay X-intercept Y-intercept Domain Range asymptote

Graphing 3 points answer  

Graphing 4 points Growth or decay Write the rule Domain Range Asymptote (0, 6) and (2, 0.375)

Graphing 4 points answer  

Properties 1 point (-4xy2)0

Properties 1 point answer (-4xy2)0 1

Properties 2 points 2b4 ⋅ 4a-3 ⋅ 5b-5 ⋅ -2a8

Properties 2 points answer  

Properties 3 points Rewrite with only one exponent: 64x3y6z12

Properties 3 points answer 64x3y6z12 These can all be written to the power of 3: 43x3(y2)3(z4)3 (4xy2z4)3

Properties 4 points Solve: 56x = 12520

Properties 4 points answer 56x = 12520 Rewrite 125 with a base of 5 56x = (53)20 56x = 560 6x = 60 X = 10

Mystery 1 point  

Sequences 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 Neighbor #1: $7(4) = $28 Neighbor #2: $0.50 + $1 + $2 + $4 = $7.50 On walk 7 your first neighbor will have given you $49 and the second neighbor will have paid you a total of $61.50

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 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 Growth or decay? Growth (b > 1) Y-intercept (also known as “a” 0.5) Rate of growth or decay b = 1.25, growing by 25% D. Growth factor: 1.25

Other 2 points (-4xy5z3)2

Other 2 points answer (-4xy5z3)2 = 16x2y10z6

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. Write an equation to model this situation. What is the domain? What is the range?

Other 4 points answer  

Write a rule to model the data. Final Jeopardy Write a rule to model the data. x 1 2 3 4 y 10 12.5 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 y = 8(1.25)x 10 = a(b)1 1.25 = b1