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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

Respuesta :

Answer:

[tex]y = Ke^{5.2t}[/tex]

Exponential growth

Step-by-step explanation:

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

We have that:

[tex]\frac{dy}{dt} = 5.2y[/tex]

So

[tex]\frac{dy}{y} = 5.2dt[/tex]

Integrating both sides

[tex]\ln{y} = 5.2t + K[/tex]

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

We apply the exponential to both sides, so:

[tex]y = Ke^{5.2t}[/tex]

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

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