Math. Increases

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In 1960, the population was 291000. In 1970, the population was 480000. Assuming exponential growth, what is the annual percent rate? and doubling time?

The answers are 5.13% and 14 years. I do not know how to get this though :( Please help!

  • Math. Increases -

    Please help! test tomorrow

  • please help. Test tomorrow -

    thanks:)

  • Math. Increases -

    Let's use the equation

    number = a e^kt, where a is the initial value, k is the rate of growth and t is the number of years

    so let 1960 correspond to a time of t = 0
    then 1970 ----> t = 10
    also a = 291000

    480000 = 291000 e^10k
    1.64948 = e^10k
    take ln of both sides
    ln 1.64948 = ln e^10k = 10k
    k = .50046/10 = .050046 = 5.005 %
    (no idea how they got their answer, it is not correct)

    check:
    291000 e^(10(.050046)) = 479999
    pretty close to 480000
    their answer:
    291000 e^(10(.0513)) = 486056 , too big

    for doubling time:

    2 = 1(e^.050046t)
    ln 2 = .050046t
    t = ln 2/.050046 = 13.8 years.

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