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If a population consists of ten thousand individuals at time t=0 (P0), and the annual growth rate (excess of births over deaths) is 3% (GR), what will the population be after 1, 15, and a 100 years (n)? Calculate the "doubling time" for this growth rate. Given this growth rate, how long would it take for this population of a hundred thousand individuals to reach 1.92 million? one equation that may be useful is:

Pt=Po * (1+ {GR/100})n

Additionally, using the current world population from the census website, calculate world population in 2100 with growth rates of 2.3% and 0.5% why is this important?

  • MATH -

    The first part of the question has been answered before. See:

    For the second part of the question, it is essentially the same idea. By using the formula
    P(t) = projected population in year t
    r = rate of growth, for example, 0.023 or 0.005

    If you need more help, post any time.

  • MATH -

    Your equation should be
    Pt=Po * (1+ {GR/100})^n
    The n is an exponent.

    Why don't you just apply the formula?

    After 100 years,
    Pt/Po = (1.03)^100 = 19.2

    Note that ratio also equals
    1.92 million/100,000

    The population doubling time is about 24 years. There is a handy approximate rule of thumb that says
    (growth rate, %)*(doubling time, years) = 72

    The exact answer is
    log2/(log 1.03) = 23.45 years

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