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

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