Question

A country's population in 1992 was 72 million. In 1998 it was 76 million. Estimate the population in 2012 using the exponential growth formula. Round your answer to the nearest million.
formual: P=Ae^kt

Answer 1

We assume the annual percentage increase is the same. We will work out the constant k using the formula

We have
P = 76
A = 72
t = 6 years (from 1992 to 1998)

Substitute into the formula
$76=72e^{6k}$
$\frac{76}{72}=e^{8k}$
Take log both sides give
$ln( \frac{76}{72})=ln(e^{6k})$
$0.05406722127=6k$
$k=0.009$

We can now work out the number of population by the end of 2012 using the formula

We have
A = 72 million
k = 0.009
t = 10 years (1992 to 2012)

$P=72e^{0.009*10}$$P=78.78$≈79 million