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Separable differential equations: Suppose a population P = P(t) grows in such a way that its rate of growth dPdtobeys the equation dPdt=P100-P

This is called a differential equation because it is an equation that involves a derivative. In the series of steps that follow, you will find a function P(t) that behaves according to this differential equation.

Use partial fractions to show that the integral on the left side of this equation is equal to1100lnP-ln100-P+C1

Short Answer

Expert verified

The given statement is proved.

Step by step solution

01

Step 1. Given information

Differential equation isdPdt=P100-P

02

Step 2. Explanation

dPdt=P100-P

Integrate both sides.

dPP100-P=dP100P-dP100100-P=1100lnP-ln100-P+C1

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