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Math Help - Population Growth

  1. #1
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    Population Growth

    The population of a midwestern city follows the exponential law. If the population decreased from 900,000 to 800,000 from 1993 to 1995, what will the population be in 1997?

    Extra: What is the population in 2008?
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  2. #2
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    Quote Originally Posted by magentarita View Post
    The population of a midwestern city follows the exponential law. If the population decreased from 900,000 to 800,000 from 1993 to 1995, what will the population be in 1997?

    Extra: What is the population in 2008?
    P = P_0 e^{kt} where t is number of years measured from start of 1993.

    At t = 0, P = 900,000 therefore P_0 = 900,000 and so P = 900,000 e^{kt}.

    Substitute t = 2, P = 800,000 and solve for k:

    800,000 = 900,000 e^{2k} \Rightarrow \frac{8}{9} = e^{2k} \Rightarrow \ln \frac{8}{9} = 2k \Rightarrow k = .... (I'd suggest getting an answer correct to five decimal places).

    Now substitute the values of t corresponding to 1997 and 2008 and solve for P in each case.
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  3. #3
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    I will...

    I will play with this question to find k.

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