Question

Determining Exponential Growth and Decay in Exercise, use the given information to write an exponential equation for y. Does the function represent exponential growth or exponential decay?

dy/dt = 5.2y, y = 18 when t = 0

Answer 1

`y = Ke^(5.2t)`

Exponential growth

Explanation:

We can solve this differential equation by the separation of variables method.

We have that:

`(dy)/(dt) = 5.2y`

So

`(dy)/(y) = 5.2dt`

Integrating both sides

`ln(y) = 5.2t + K`

In which K is the value of y when t = 0.

We apply the exponential to both sides, so:

`y = Ke^(5.2t)`

This is our exponential equation. Since the power of e is a positive value, the function represents exponential growth.