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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

1 Answer

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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


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