Chapter 8.2, Problem 56ES

Suppose that the growth of a population $y=y\left(t\right)$ is given by the logistic equation

$y=\frac{1000}{1+999e^{-0.9t}}$

(a) What is the population at time $t=0?$

(b) What is the carrying capacity L?

(c) What is the constant k?

(d) When does the population reach $75\%$ of the carrying capacity?

(e) Find an initial-value problem whose solution is $y\left(t\right).$