Lesson Worksheet: Exponential Growth and Decay Models Mathematics • 9th Grade

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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.

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 days’ time.

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.

Q5:

Let the population of a city be . If the population increases by each year, what will the population of the city be in nine years’ time?

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 engine’s 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

Q7:

The number of tourists visiting a theme park increases every year and can be found using the equation , where million is the number of visitors years after 2010. If the number of visitors continues to increase at the same rate, in what year will the park first reach 2 million visitors?

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

Q9:

On July 5, green algae was found on the bottom of a swimming pool whose width is 6 m and length is 12 m. If the area, in mm², the algae covers days later is given by , when will the algae completely cover the bottom of the swimming pool?

AJuly 15
BSeptember 15
CAugust 22
DAugust 18
EJuly 18

Q10:

Noah’s 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?

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