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Math Help - study question, Alg II

  1. #1
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    study question, Alg II

    I am having major issues with this problem, even with starting it. I have a test coming up and this is an example. I actualy have 3 questions but this is the first.

    The population of a midwestern city follows the exponential law.
    a.) If N is the population of the city and t is the time in years, express N as a function of t.

    b.) If the population decreased from 800,000 to 700,000 from 2003 to 2005, what will be population in 2007.
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  2. #2
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    Quote Originally Posted by Toddry View Post
    I am having major issues with this problem, even with starting it. I have a test coming up and this is an example. I actualy have 3 questions but this is the first.

    The population of a midwestern city follows the exponential law.
    a.) If N is the population of the city and t is the time in years, express N as a function of t.

    b.) If the population decreased from 800,000 to 700,000 from 2003 to 2005, what will be population in 2007.
    I believe the population exponential rule is P = (Po)e^(kt)
    where Po = initial P
    k = any rational number
    t = time

    So from 2003 to 2005,
    t = 2 years
    Po = 800,000
    P = 700,000
    k = ?

    700,000 = 800,000e^(k*2)
    e^(2k) = 700,000 /800,000 = 7/8
    2k *ln(e) = ln(7/8)
    k = ln(7/8) /2
    k = -0.066766

    Then, from 2003 to 2007,
    t = 4 years
    Po = 800,000
    P =?
    k = -0.066766

    Can you solve for P now?
    You should get P = 612,500
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  3. #3
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    Quote Originally Posted by ticbol View Post
    I believe the population exponential rule is P = (Po)e^(kt)
    where Po = initial P
    k = any rational number
    t = time

    So from 2003 to 2005,
    t = 2 years
    Po = 800,000
    P = 700,000
    k = ?

    700,000 = 800,000e^(k*2)
    e^(2k) = 700,000 /800,000 = 7/8
    2k *ln(e) = ln(7/8)
    k = ln(7/8) /2
    k = -0.066766

    Then, from 2003 to 2007,
    t = 4 years
    Po = 800,000
    P =?
    k = -0.066766

    Can you solve for P now?
    You should get P = 612,500
    I am going to check it now. Thank you much. I am coming up with a lot of the same. Sometimes its hard to start these.
    Last edited by Toddry; October 7th 2008 at 05:26 AM.
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