Lesson Worksheet: Exponential Growth and Decay Models Mathematics • 9th Grade
In this worksheet, we will practice modeling exponential growth and decay arising from the differential equation y′=±ky.
Q1:
A mathematical model predicts that the population of a country, million, will be given by the formula , where is the number of years since 2015. Use this model to predict the population of the country, to the nearest million, in both 2021 and 2022.
- A18 million, 21 million
- B19 million, 21 million
- C18 million, 19 million
- D19 million, 20 million
- E18 million, 20 million
Q2:
Chloe wants to invest some money. She would like the value of her investment to double in 10 years. Write an equation that can be used to find , the annual rate of interest required. Assume interest is compounded annually.
- A
- B
- C
- D
- E
Q3:
A population of fruit flies quadruples every 3 days. Today, there were 150 fruit flies in the population under investigation.
Assuming the population continues to grow at the same rate, write an equation that can be used to find , the number of fruit flies expected to be in the population in daysβ time.
- A
- B
- C
- D
- E
Q4:
The population of Malawi, in millions, is modeled by the exponential function , where is the time in years since January 1, 1960.
To the nearest month, how long does it take for the population to double?
- A24 years, 3 months
- B21 years, 4 months
- C26 years
- D27 years, 2 months
- E21 years
Which year will be the first to start with a population of more than 20 million?
Find the function that represents the same exponential model, but with the input now being the time in years since January 1, 2000. Express this function using a base of 2 rather than the previously used 1.029.
- A
- B
- C
- D
- E
Q6:
The number of users of a new search engine is increasing every month and can be found using the equation , where represents the number of users and represents the number of months since the search engineβs launch. If the search engine was launched on the 1st of March, in which month would the search engine have 2,000 users?
- AOctober
- BSeptember
- CAugust
- DNovember
- EJune
Q8:
Rewrite in the form , with to two decimal places. What is the significance of the number ?
- A is the number of years it takes for the population to double
- B is the number of years it takes for the population to triple
- C is the number of years it takes for the population to double
- D is the number of years it takes for the population to triple
- E is the number of years it takes for the population to double
Q10:
Noahβs bank account gives him interest on his balance each month. He models his balance after months with the recursive formula . If his initial deposit is 450.00, after how many months will his balance be greater than $600?