Chapter 6.4, Problem 16E

(a)

To determine

To calculate: The value of k of the logistic differential equation is, $\frac{dP}{dt}=0.5P\left(1-\frac{P}{250}\right)$

(b)

To determine

To calculate: The value of carrying capacity of the logistic differential equation is, $\frac{dP}{dt}=0.5P\left(1-\frac{P}{250}\right)$

(c)

To determine

To graph: The slope field of the logistic differential equation $\frac{dP}{dt}=0.5P\left(1-\frac{P}{250}\right)$

(d)

To determine

To calculate: The value of P at which the population growth rate is greatest for the logistic differential equation is, $\frac{dP}{dt}=0.5P\left(1-\frac{P}{250}\right)$