# Math Help - Homework help fast...please

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

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

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

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

$103200 = 81500e^{7r}$

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

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

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