# What is the differential equation that models exponential growth and decay?

The simplest type of differential equation modeling exponential growth/decay looks something like:

This situation translates into the following differential equation:

First step in solving is to separate the variables:

Now, we will simply integrate:

The right side is fairly easy. Remember the constant of integration:

And now this is easily solved:

Exponentiate both sides:

This can be rewritten as:

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The differential equation that models exponential growth and decay is:

dy/dt = ky

Where:

- dy/dt represents the rate of change of the quantity y with respect to time t.
- k is a constant representing the growth rate (if positive) or decay rate (if negative) of the quantity y.

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