CPM Homework Help : CALC Problem 10-67

The rabbits in your neighbor's backyard are reproducing at a rate proportional to the number present. Today there are $32$ rabbits. Two weeks ago there were only $20$ . When will there be $200$ rabbits?

Step 1:

If $P =$ rabbit population, then:
Use separation of variables then integrate to obtain:
$P=Ce^{kt}$

Step 2:

Solve for $C$ and $k$ :
Solve for $t$ :
$200=32e^{-0.5\ln(20/32)t}$