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Math Help - World population...

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    32

    World population...

    hey guys,

    I hate to keep bugging you all but I'm having some difficulties with this question. It's annoying because I followed my notes exactly and still got the answer wrong.

    Here's the question:

    The table gives estimates of the world population, in millions, from 1750 to 2000.

    Year Population
    1750 790
    1800 980
    1850 1260
    1900 1650
    1950 2560
    2000 6080

    (a) Use the exponential model and the population figures for 1750 and 1800 to predict the world population in 1900 and 1950.

    This is what I attempted:

    So, 1750: 790 mil and 1800: 980 mil

    P(t) = P(o) * e^kt
    980 = 760 * e^k(50) because 1800-1750 = 50 years
    980/760 = e^k(50)
    1.289 = e^k(50)

    ln(1.289)/50 = k
    0.005=k (0.5%)

    so, P(t) = 760 * e^0.005t

    Then, to solve for 1900:

    P'(150)=760*e^0.005(150) * 0.005 (note: 150 comes from 1900-1750 = 150 years in between - I'm following what my prof. did, and this is what he did so...)
    P'(150)=8 million

    I'm not sure what I'm doing wrong. I know that 8 mil is way too low (or, at least it seems like it compared to all the other values that the table gave).

    Any help's appreciated! Thanks.
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  2. #2
    Senior Member
    Joined
    Dec 2008
    Posts
    319
    What you found is the rate of change of the population per year. To find the population itself, we simply find the value of P(t) at t=150:

    P(150)=760e^{0.005\cdot150}.
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