Math AP Calc

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In 1951, the population of India was 357 million people. By 1981 it had grown to 984 million. If the population is growing exponentially, when (in what month of what year) will the population reach 1 billion people?

  • Math AP Calc -

    let the equation be

    P = 357(e)^(kt) where t is the time in years since 1951

    so 1981 ---> t = 30

    984 = 357(e^30k)
    2.756303 = e^30k
    30k = ln 2.756303
    k = .0337963

    so now we have P = 357(e^.0337963t)

    so 1000 = 357(e^.0337963t)
    2.80112 = e^.0337963t
    t = 30.477
    30 years + .477 of the next year
    30 yrs + 5.7 months
    or
    in the 6th month of 1951

  • Math AP Calc -

    wouldn't it be past 1981 instead of in the 6th month of 1951?

  • Math AP Calc -

    of course, clearly a typo. Sorry about that.

    since my t=30.477 and I defined as 1951 as t=0
    the time is 1951 + 30.477 = 1981 + .477yrs.

  • Math AP Calc -

    Does the .477 years mean the 6th month (June) you were talking about?

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