algebra

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I have no clue where to begin on this problem. Can some one help me please.


One demographer believes that the population growth of a certain country is best modeled by the function P (t) =15 e^.08t, while a second demographer believes that the population growth of that same country is best modeled by the function P (t) =15 +3t. In each case, t is the number of years from the present and P (t) is given in millions of people. For what values of t do these two models give the same population? In how many years is the population predicted by the exponential model twice as large as the population predicted by the linear model?

  • algebra -

    Just get past the words and see what they're really telling you.

    There are two functions:
    p(t) = 15e^.08t
    q(t) = 15 + 3t

    when are they equal?

    15e^.08t = 15+3t

    p(0) = 15
    q(0) = 15

    p(1) = 16.249
    q(1) = 18
    They start out the same, but you know that the exponential will eventually grow much faster. Look at a graph.

    p(t) = q(t) when t = 20.235 or so

    when does

    p(t) = 2q(t)
    again, from the graph, t=34.501

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