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

In this lesson, we will learn how to model exponential growth and decay arising from the differential equation y′=±ky.

Lesson Plan

Students will be able to

solve differential equations of the form with given initial conditions,
understand how the differential equation models natural growth and decay,
solve real-world problems involving exponential growth and decay.

Lesson Video

Lesson Playlist

03:48
04:51
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03:26

Lesson Worksheet

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.

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.