# A county's population in 1991 was 147 million. In 1998 it was 153 million. Estimate the population in 2017 using the exponential growth formula. Round your answer to the nearest million.

QUESTION POSTED AT 02/06/2020 - 01:21 AM

QUESTION POSTED AT 02/06/2020 - 01:21 AM

Let t=number of years since 1991.

Then

P(t)=147 e^(kt) ... in millions

P(0)=147 e^(0)=147

P(7)=147 e^(7k)=153

e^(7k)=(153/147)

take ln both sides

ln(e^(7k))=ln(153/147)

7k=0.0400 => k=0.005715

Year 2017=>t=2017-1991=26

P(26)=147e^(26*.005715)=170.55

Answer: in 2017, the projected population is 170.55 millions.

Then

P(t)=147 e^(kt) ... in millions

P(0)=147 e^(0)=147

P(7)=147 e^(7k)=153

e^(7k)=(153/147)

take ln both sides

ln(e^(7k))=ln(153/147)

7k=0.0400 => k=0.005715

Year 2017=>t=2017-1991=26

P(26)=147e^(26*.005715)=170.55

Answer: in 2017, the projected population is 170.55 millions.

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