Exponential Decay and Growth Problems

Given the function f(x) = 1.00005^x, what is the rate of change?

• .0005%

• .005%

• .05%

• .5%

Given the function f(x) = 0.92^x, what is the rate of change?

• .92%

• 9.2%

• .08%

• 8%

Given the function f(x) = 0.45^x, what is the rate of change?

• 45%

• 55%

• 4.5%

• 5.5%

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 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

Given f(x) = (1.09)⁴⁵ and the rate of change is 9% every minute, how much time has passed?

• 9 minutes

• 5 minutes

• 45 minutes

• 9 times 45 minutes

• Linear Growth

• Linear Decay

• Exponential Growth

• Exponential Decay

• Because the 25 was bigger than one

• Because the 0.20 was bigger than one

• Because the 25 was less than one

• Because the 0.20 was less than one

A flea medicine breaks down at a rate of 20% per hour. This is the rate of decay of the medicine. The initial dose is 60 milligrams. Which of the following represent the equation the models the amount of flea medicine left in an animal?