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

Answer:

$y = Ke^{5.2t}$

Exponential growth

Step-by-step explanation:

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

We have that:

$\frac{dy}{dt} = 5.2y$

So

$\frac{dy}{y} = 5.2dt$

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.