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Thread: Homework help fast...please

  1. #1
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    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?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Jenny Service View Post
    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)
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    answer

    thank you! that really does help
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