Question

A country's population in 1994 was 182 million.In 2002 it was 186 million. Estimatethe population in 2004 using the exponentialgrowth formula. Round your answer to thenearest million.

Answer 1

we have the exponential formula

`P=Ae^((kt))`

so

we have

A=182 million ------> initial value (value of P when the value of t=0)

The year 1994 is when the value ot t=0

so

year 2002 -----> t=2002-1994=8 years

For t=8 years, P=186 million

substitute the value of A in the formula

`P=182e^((kt))`

Now

substitute the values of t=8 years, P=186 million

`\begin{gathered} 186=182e^((8k)) \\ e^((8k))=(186)/(182) \\ \text{apply ln both sides} \\ 8k=\ln ((186)/(182)) \\ k=0.0027 \end{gathered}`

the formula is equal to

`P=182e^((0.0027t))`

Estimate the population in 2004

t=2004-1994=10 years

substitute the value of t in the formula

`\begin{gathered} P=182e^((0.0027\cdot10)) \\ P=187 \end{gathered}`

therefore

the answer is 187 million