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The population of the world in 1987 was 5 billion and the annual growth rate was
estimated at 2 percent per year. Assuming that the world population follows an
exponential growth model, find the projected world population in 2015.

  • maths -

    Assume formula
    Population in billions at time t (counting from 1987) as
    P(t)=Ae^(kt)
    where A and k are constants.
    At t=0 (1987),
    P(0)=Ae^(0)=A=5
    the formula becomes:
    P(t)=5e^(kt)
    P(1)=5*1.02=5e^(kt) [t=1]
    =>
    e^(k)=1.02 [t=1]
    Take log both sides
    k=log(1.02) [natural log]

    So
    P(t)=5e^(t*log(1.02))
    where log(1.02)=0.0198 approx.

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