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Math Help - Applications of exponential equations

  1. #1
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    Applications of exponential equations

    I have two problems on my test review that I have no idea where to start.

    1.) The population of Merchantville was 20,000 in 1990 and 25,000 in 1995. If exponential growth is assumed, find a model for the population growth and then use the model to determine the population in 2008.


    2.) A sample of 500 grams of radioactive lead 210 decays to polonium 210 according to the function A(t)=500e^-.032(t), where t is in years. Find the amount of the sample remaining after half-life.

    Thanks in advance!
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  2. #2
    MHF Contributor
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    1.) The population of Merchantville was 20,000 in 1990 and 25,000 in 1995. If exponential growth is assumed, find a model for the population growth and then use the model to determine the population in 2008.


    Let A = initial amount
    And B = final amount
    And t = time in years

    You can use
    1) B = A*a^t
    or 2) B = A*e^(kt)
    to get the same answer.

    A = 20,000
    B = 25,000
    t = 1995 -1990 = 5 yrs
    So,
    25,000 = 20,000a^5
    5ln(a) = ln(25,000/20,000)
    ln(a) = ln(25/20) /5 = 0.04462871
    a = e^0.04462871 = 1.045639553

    Hence,
    B = A*(1.045639553)^t

    So in 1998, say, based from 1995, where t = 3,
    C = 25,000(1.045639553)^3 = 28,582 ---------------answer.


    2.) A sample of 500 grams of radioactive lead 210 decays to polonium 210 according to the function A(t)=500e^-.032(t), where t is in years. Find the amount of the sample remaining after half-life.

    Not very clear.
    Does that mean the half-life of Lead 210, or of Polonium 210? Are those two materials the same in half-lives?
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