Exponential Growth and Decay Equations

A tennis tournament begins with 128 players. At the end of round one, there will be 64 players. There are 32 players at the end of round 2 and 16 players remaining after round 3. Write the equation that best models this situation.

• y = -64x + 128

• y = 0.5x + 128

• y = 128(0.5)^x

• y = 128(2)^x

Write an exponential function to model the situation. The cost of tuition at a college is $12,000 and is increasing at a rate of 6% per year.

• C(t) = 12000(.94)^t

• C(t) = 12000(1.94)^t

• C(t) = 12000(.06)^t

• C(t) = 12000(1.06)^t

The amount of cola in a soda machine decreases by a rate of 5% each hour. The amount of cola in the machine was originally 75 gallons.

Which function models the amount of cola in gallons after h hours?

• f(h) = 75(-5)^h

• f(h) = -5(75)^h

• f(h) = .95(75)^h

• f(h) = 75(.95)^h

The function y = 24,220 (0.85)^x represents Mr. Bittle's investment in the stock exchange where x is measured in months.

Which statement is NOT true.

• Mr. Bittle loses 85% of his investment monthly

• Mr. Bittle initially invested $24,220

• Each month Mr. Bittle loses 15% of his investment

Write an exponential function to model the situation. You invest $1500. Your investment escalates at a rate of 3.5%.

• B(t) = 1500(0.965)^t

• B(t) = 1500(1.035)^t

• B(t) = 1500(.035)^t

• B(t) = 1500(1.965)^t

Write an exponential function to model the situation. The value of a car is $18000 and is depreciating at a rate of 12% per year.

• V(t) = .88(18000)^t

• V(t) = .12(18000)^t

• V(t) = 18000(.88)^t

• V(t) = 18000(.12)^t

What is the a-value (or y-intercept) for the function: f(x) = 800(0.85)^x?

• 800

• 0.85

• 0.15

• x

What is the decay rate for the function: f(x) = 800(0.85)^x?

• 800

• 0.85

• 15%

• x

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the decay rate?

• ^0.08

• ^1.08

• 0.92

• 8%

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the exponential equation that models this situation?

• y = 8(15,000)^x

• y = 15,000(1.08)^x

• y = 15,000(0.92)^x

• y = 15,000(0.08)^x