SOLUTION: The population of the United States tends to grow at a rate proportional to the size of the population. Thus we may represent the population size by the exponential model A(t) = 18

Question 91591: The population of the United States tends to grow at a rate proportional to the size of the population. Thus we may represent the population size by the exponential model A(t) = 180e^0.013t, where t is the number of years since 1960 and A(t) is the population in millions. In what year will the population of the United States exceed one billion?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Thus we may represent the population size by the exponential model A(t) = 180e^0.013t, where t is the number of years since 1960 and A(t) is the population in millions. In what year will the population of the United States exceed one billion?
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180e^0.013t = 10^9
e^0.013t = 10^9/180
Take the natural log of both sides to get:
0.013t ln(10^9)-ln(180)
t = [9ln(10)-ln(180)]/0.013
t = 1086.98
The year this will happen is 1960 + 1086.98 = 3047
Cheers,
Stan H.
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