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Math Help - rate of population growth!

  1. #1
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    Exclamation rate of population growth!

    The population P of a town has a rate of change proportional to the difference between P and 15,000. This may be expressed as dP/dt = k(P - 15000), where k = 0.2 and t = time in years. Find the population after one year

    here is how I decided to do it. can someone please check?

     P = 15,000 + Ae^{0.2t}

    initially,

     21,000 = 15,000 + Ae^{0.2t}

     6,000 = Ae^{0}

    6,000 = A

    P = 15,000 + 6000e^{0.2t}

    when t = 1

     P = 15,000 + 6000e^{0.2}

     = 22328

    this is not the answer. the answer is 22,000.


    what did i do wrong?
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  2. #2
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    Quote Originally Posted by differentiate View Post
    The population P of a town has a rate of change proportional to the difference between P and 15,000. This may be expressed as dP/dt = k(P - 15000), where k = 0.2 and t = time in years. Find the population after one year

    here is how I decided to do it. can someone please check?

     P = 15,000 + Ae^{0.2t}

    initially,

     21,000 = 15,000 + Ae^{0.2t}

     6,000 = Ae^{0}

    6,000 = A

    P = 15,000 + 6000e^{0.2t}

    when t = 1

     P = 15,000 + 6000e^{0.2}

     = 22328

    this is not the answer. the answer is 22,000.


    what did i do wrong?
    Do you have the right initial condition? You didn't specify it in the question...
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  3. #3
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    ohh sorry, I forgot. It was:

    If the population at the beggining of 1960 was 21,000, find the population after one yaer
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  4. #4
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    I can't see anything wrong with your working out, I keep getting the same answer.
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  5. #5
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    alright thanks man. The book I'm working on keeps having incorrect answers!
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