Exponential Growth and Decay Practice

Multiple Choice

If the decay rate is 20%, which of the following represent the decay factor?

• 0.2

• 0.8

• 1.2

• 1.8

Multiple Choice

If the growth rate is 80%, what is the growth factor?

• 0.2

• 0.8

• 1.2

• 1.8

Multiple Choice

 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?

• $$y=60\left(.2\right)^x$$  

• $$y=20\left(60\right)^x$$  

• $$y=60\left(.8\right)^x$$  

• $$y=60\left(1.2\right)^x$$  

Multiple Choice

Penicillin decays exponentially in the human body. Suppose you receive a 300-milligram dose of penicillin to combat strep throat. About 180 milligrams will remain active in your body after 1 day. Which equation represents the amount of penicillin remaining in your body?

• $$y=300\left(0.6\right)^x$$

• $$y=300\left(1.6\right)^x$$

• $$y=300\left(1.67\right)^x$$

• $$y=300\left(0.4\right)^x$$

Multiple Choice

The original value of a painting is $1400, and the value increases by 9% each year. Write an exponential growth function to model this situation.

• y=1400(1.09)^x

• y=1.09(1400)^x

• y=1400(.91)^x

• y=1.09^x

Multiple Choice

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

• y = 15(35)^x

• y = 15(1.35)^x

• y = 15(0.35)^x

• y = 35(1.15)^x

Multiple Choice

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

• y=6(0.14)^x

• y=6(1+14)^x

• y=6(1.14)^x

• y=6(0.86)^x

Multiple Choice

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

Multiple Choice

Since January 1980, the population of the city of Brownville has grown according to the mathematical model y=720,500(1.022)^x, where x is the number of years since January 1980. What is the percentage increase of the population annually?

• 720,500%

• 102.2%

• 2.2%

• 22%

Multiple Choice

Which value represents the y-intercept?  $$f\left(x\right)=\frac{1}{2}\cdot3^x$$  

• $$\frac{1}{2}$$   

• 3

• x

• f(x)

Multiple Choice

What is shown in this graph?

• Growth

• Decay

• Neither

Multiple Choice

Which value represents the starting value? $$y=3\cdot\frac{1}{2}^x$$

• 3

• $$\frac{1}{2}$$  

• y

• x

Multiple Choice

This function represents the number of ants in a colony $$f\left(x\right)=3\ \left(\ 2\right)^x$$ How many ants did you begin with? 

• There was 2 ants

• There was 3 ants

• The equation doesn't tell us

Multiple Choice

This function represents the number of ants in a colony $$f\left(x\right)=3\ \left(\ 2\right)^x$$ What is the growth rate?

• The ants are growing by 3 times

• The ants are growing by 2 times

• The equation doesn't tell us

Multiple Choice

Jack invest $600 earning 5% interest rate. How much will he have after 5 years?

• $630

• $729.30

• $765.77

• $4556.25