Chapter 6.3, Problem 54E

(a)

To determine

To calculate: Value of k for the given logistic equation $P\left(t\right)=\frac{5000}{1+39e^{-0.2t}}$.

(b)

To determine

To calculate: The value of the carrying capacity of the given logistic equation $P\left(t\right)=\frac{5000}{1+39e^{-0.2t}}$.

(c)

To determine

To calculate: The value of the initial population of the given logistic equation $P\left(t\right)=\frac{5000}{1+39e^{-0.2t}}$.

(d)

To determine

To calculate: The time at which the population will become $50\%$ of its carrying capacity of the logistic equation $P\left(t\right)=\frac{5000}{1+39e^{-0.2t}}$.

(e)

To determine

To calculate: The logistic differential equation of the given logistic equation $P\left(t\right)=\frac{5000}{1+39e^{-0.2t}}$.