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)`

`(76)/(72)=e^(8k)`
Take log both sides give

`ln( (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