Suppose a certain population satisfies the logistic equation given by dp
dt = 10p − p
2 with p(0) = 1.
determine the population when t = 3

The population when t = 3 is 10.

Step-by-step explanation:

Suppose a certain population satisfies the logistic equation given by

with P(0)=1. We need to find the population when t=3.

Using variable separable method we get

Integrate both sides.

            .... (1)

Using partial fraction

Using these values the equation (1) can be written as

On simplification we get

We have P(0)=1

Substitute t=0 and P=1 in above equation.

The required equation is

Multiply both sides by 10.

Reciprocal it

The population when t = 3 is

Using calculator,

Therefore, the population when t = 3 is 10.

step-by-step explanation: