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Math Help - Integral of the reciprocal Function

  1. #1
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    Integral of the reciprocal Function

    Hi guys, its my first post here...hoping you guy can help me solve this problem...


    Population Problem: Population of a community is growing at a rate of 5% per year.

    DP/DT = .05P

    Suppose the population, P, is 1000 at time t=0, and grows to P=N at t=10, where you must fine the value of N. By separating the variables and then integrating you get,

    1/p Dp = .05dt

    N 10
    1 DP = .05dt
    p
    1000 0


    Evaluate the integral numerically for N= 1000, 1500, 2000, 2500, 500, and 100.
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  2. #2
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    Quote Originally Posted by sacsha1 View Post

    Suppose the population, P, is 1000 at time t=0, and grows to P=N at t=10, where you must fine the value of N. By separating the variables and then integrating you get,

    1/p Dp = .05dt

    N 10
    1 DP = .05dt
    p

    sacsha1, you did not finish the integration

    \int \frac{dp}{p} = \int \frac{dt}{2}

    gives

    \ln(p) = \frac{t}{2}+c

    p = e^{\frac{t}{2}+c}

    p = Ae^{\frac{t}{2}}


    Now use p(0)=1000 to find A
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