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
Worksheet: 25 Questions • 1 Video
The number of cars worldwide, years after 2015, can be modeled by the formula . In what year will there be 1.4 billion cars worldwide?
Let be the population of bacteria in a culture. At time , the population is 4 million. Suppose that, after hours, the bacteria grow at the instantaneous rate of change of million bacteria per hour. Estimate the number of bacteria at time in millions to two decimal places.
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 where represents the number of atoms remaining after seconds. The proportionality constant is considered the decay constant for this process. If represents the number of remaining atoms at seconds, find the general solution.