# Lumyn Electronics has seen stellar expansion in recent months. The company's profit, P, is...

## Question:

Lumyn Electronics has seen stellar expansion in recent months. The company's profit, {eq}P{/eq}, is currently growing exponentially at {eq}5\%{/eq} each year. The rate of change of the company's profit can be modeled as {eq}\frac{1}{P} dP = 0.05dt{/eq}. Find a general formula that expresses the profit of the company as a function of time, {eq}t{/eq}.

## Differential Equation:

We will use the variable separable form to solve the differential equation where we will integrate with respect to P and t separately and then find the value of constant.

## Answer and Explanation:

To find a general formula we will use the varibale separble form:

{eq}\frac{dP}{P}=0.05dt {/eq}

Now integrating both sides:

{eq}\int \frac{dP}{P}=0.05\int dt\\ \ln P=0.05t+c {/eq}

Rewriting it we get:

{eq}P=e^{0.05t+c} {/eq}

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from GRE Math: Study Guide & Test Prep

Chapter 16 / Lesson 1