CPM Homework Help : APCALC Problem 10-84

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:

$\frac{dP}{dt}=kP$

Step 2:

Use separation of variables then integrate to obtain:

$P=Ce^{kt}$

Step 3:

Solve for $C$ and $k$ :

$32=Ce^{0k}\text{ and }20=Ce^{-2k}$

Step 4:

Solve for $t$ :

$200=32e^{-0.5\ln(20/32)t}$