Question

what is the doubling time for this population of alligators?

Answer 1

We will have the following:

In order to determine the number of years from the time of introduction in which the population would double, we will proceed as follows:

$2(319)=(319)(2)^{\frac{t}{3}}\Rightarrow638=319(2)^{\frac{t}{3}}$$\Rightarrow\frac{638}{319}=2^{\frac{t}{3}}\Rightarrow2=2^{\frac{t}{3}}$$\Rightarrow\ln (2)=\frac{t}{3}\ln (2)\Rightarrow\frac{\ln (2)}{\ln (2)}=\frac{t}{3}$$\Rightarrow1=\frac{t}{3}\Rightarrow t=3$

So, the number of years it would take for the population of alligators to double would be 3 years.