2. First-Order Equations I

Logistic Models — Quiz

Test your understanding of logistic models with 5 practice questions.

Practice Questions

Question 1

In the logistic model $P(t)=\frac{K}{1+Ae^{-rt}}$, what does $K$ represent?

Question 2

Which statement best describes logistic growth?

Question 3

For the differential equation $\frac{dP}{dt}=rP\left(1-\frac{P}{K}\right)$ with $r>0$ and $K>0$, which values are equilibrium solutions?

Question 4

In a logistic model, the population growth rate is greatest when $P$ equals what value?

Question 5

Suppose $P(t)=\frac{K}{1+Ae^{-rt}}$ and $P(0)=20$ with $K=100$. What is $A$?