Exponential Functions Review

Which of the following conversions are correct? Check all that apply.

• 45% = 0.45

• 37.5% = 0.375

• 120% = 1.20

• 5.7% = .57

Which of the following exponential equations/scenarios shows DECAY? Check all that apply.

• $y=20\left(0.75\right)^x$

• $y=0.25\left(5.7\right)^x$

• Jules is investing $2000 into an account that compounds interest monthly at a rate of 4.5%

• The value of Macy's new car depreciates at a rate of 20% each year.

Margaret is researching cell reproduction. She observes 15 cells, and estimates the number of cells grows by a rate of 21% each hour. Which equation could model this situation?

• $y=15\left(.21\right)^x$

• $y=15\left(1.21\right)^x$

• $y=21\left(1.15\right)^x$

• $y=15\left(1-.21\right)^x$

Mabel is modeling the population of her town, and writes an exponential model of  $y=23000\left(1.0152\right)^x$ , where x is years after 2000. Which of the following statements is true? Check all that apply. 

• The growth rate of the town is 1.52%

• The population of the town is decreasing. 

• There were 23,000 people in the town in 2000. 

• The model represents a linear relationship. 

Mabel is modeling the population of her town, and writes an exponential model of  $y=23000\left(1.0152\right)^x$ , where x is years after 2000. Predict the number of people in her town in 2021. 

• 10,152 people

• 23,000 people
  

• 31,573 people
  

• 40,043 people
  

Mabel is modeling the population of her town, and writes an exponential model of  $y=23000\left(1.0152\right)^x$ , where x is years after 2000. In what year will the population reach 40,000 people?

• Between 2001 - 2002

• Between 2036 - 2037

• Between 2043 - 2044

• Never, according to this model 

Which of the following equations represents interest compounded continuously?

• $A=300e^{0.023t}$

• $A=300\left(1.023\right)^t$

• $A=300\left(1+\frac{.023}{12}\right)^{12t}$

• $A=300\left(1+\frac{.023}{4}\right)^{4t}$

Mo is investing $200 in a savings account, where the 4.3% interest rate is compounded monthly. How much money will be in their account in 10 years? Round to the nearest whole dollar.

Mo uses the equation  $A=P\left(1+\frac{.043}{12}\right)^{12t}$ to model their investment. What does P need to be in order for their investment to reach $400 after 10 years? Round to the nearest dollar. 

An exponential equation goes through the points (0,5) and (3, 40). Which equations could model this exponential function?

• $y=5\left(3\right)^x$

• $y=5\left(40\right)^x$

• $40=5\left(b\right)^3$

• $y=5\left(2\right)^x$