Answer
a) Carrying capacity is 100
b) Slopes are close to 0 at 100 and 0, and are largest at around 150. Solutions are increasing in interval $0
Work Step by Step
a)
$\displaystyle \frac{dP}{dt}=0.05P-0.0005P^2$
Factor to get the logistic differential equation:
$\displaystyle \frac{dP}{dt}=0.05P(1-\frac{P}{100})$
$M=100$, and so carrying capacity is 100.
b) Slopes are close to 0 at 100 and 0, and are largest at around 150. Solutions are increasing in interval $0
