Question

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?

Answer 1

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