Lesson: Exponential Growth and Decay Models

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

Sample Question Videos

  • 01:19

Worksheet: 25 Questions • 1 Video

Q1:

The number of cars worldwide, 𝑡 years after 2015, can be modeled by the formula 𝑁 = 1 0 ⋅ 𝑒 . In what year will there be 1.4 billion cars worldwide?

Q2:

Let 𝐹 ( 𝑡 ) be the population of bacteria in a culture. At time 𝑡 = 0 , the population is 4 million. Suppose that, after 𝑡 hours, the bacteria grow at the instantaneous rate of change of 3 million bacteria per hour. Estimate the number of bacteria at time 𝑡 = 1 in millions to two decimal places.

Q3:

The rate at which a radioactive substance decays is proportional to the remaining number of atoms. The differential equation which can be used to describe this process follows d d 𝑁 𝑡 = − 𝜆 𝑁 , where 𝑁 represents the number of atoms remaining after 𝑡 seconds. The proportionality constant 𝜆 is considered the decay constant for this process. If 𝑁 represents the number of remaining atoms at 𝑡 = 0 seconds, find the general solution.

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