### Home > APCALC > Chapter 12 > Lesson 12.1.2 > Problem12-25

12-25.

Given the logistic differential equation from problem 12-24, determine the size of the population when it is changing most rapidly. What is the significance of this value?

This occurs when $dP/dt$ is a maximum. Or, when $d^2P/dt^2 = 0$.

$\frac{1}{400}(800-2P)=0$

The carrying capacity is $800$ sea lions.