a populaton increases from 81,500 to 103,200 over a 7 year period. If the growth rate remians the same how long will it take the initial population to double?

2. Originally Posted by Jenny Service
a populaton increases from 81,500 to 103,200 over a 7 year period. If the growth rate remians the same how long will it take the initial population to double?
assuming exponential growth, we have

$\displaystyle P(t) = P_0 e^{rt}$

where $\displaystyle P(t)$ is the population after time $\displaystyle t$, $\displaystyle P_0$ is the initial population, $\displaystyle r$ is the rate of growth, and $\displaystyle t$ is time

since it grows from 81,500 to 103,200 over a 7 year period, we have:

$\displaystyle 103200 = 81500e^{7r}$

solve that for $\displaystyle r$, that will give you the rate of growth.

then use it to find what they asked you for, which would be to solve:

$\displaystyle 2P_0 =P_0 e^{rt}$ for $\displaystyle t$ (you will know the value of $\displaystyle r$ at this point, the value of $\displaystyle P_0$ is immaterial)