Exponential Word Problems Find the Decay or Growth

Given f(x) = (1.11)¹⁸ and the rate of change is 11% every day, how much time has passed?

• 11 days

• 18 days

• 1.11 times 18 days

• Underterminable

Given f(x) = (1.0023)³⁶ and the rate of change is 0.23% every hour, how many minutes have passed?

• 36

• 60

• 2160

• 3600

The population in Haywardsville is decreasing at a rate of 2.5% per year. If the population in 2000 was 28,000, what will be the expected population in 2015 if this rate of decrease continues? (Verbal Question: How do we know this is growth or decay?)

• 19,153

• 19,285

• 18,956

• 19,172

The population of a small town is 1600 and is increasing at a rate of 3% per year. Write an exponential function to model this situation. Then find the population of the town after 10 years. (Verbal Question: How do we know this is growth or decay?)

• f(t) = 1600(1.03)^t; 2,150 people

• f(t) = 1600(0.97)^t; 1,738 people

• f(t) = 1600(1.03)^t; 2,128 people

• f(t) = 1600(0.97)^t; 1,819 people

The value of a book is $58 and depreciates at a rate of 7% per year. Write an exponential function to find the value of the book after 8 years. (Verbal Question: How do we know this is growth or decay?)

• f(t) = 58(0.93)^t; $32.46

• f(t) = 58(1.07)^t; $76.32

• f(t) = 58(0.93)^t; $34.26

• f(t) = 58(1.07)^t; $73.62

Given the function f(x) = 1.07^x, how do you know this is an exponential function?

• Because the variable is in the exponent

• Because the base has a decimal in it

• Because f(x) is there

• Because my teacher told me

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

• C(t) = 1.06(12000)^t

• C(t) = 12000(.06)^t

• C(t) = 12000(.06)^t

• C(t) = 12000(1.06)^t

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

• y=5000(0.7)^x

• y=30(5000)^x

• y=5000(1.3)^x

• y=5000x^x

A particular type of cell triples in number every hour. Which function can be used to find the number of cells present at the end of h hours if there are initially 6 of these cells?

• f(h) = 3(6)^h

• f(h) = 6x^h

• f(h) = 6(3)^h

• f(h) = 3(6h)

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