Question

Finding a final amount in a word problem on exponential growt...A city has a population of 220,000 people. Suppose that each year the population grows by 5.25%. What will the population be after 13 years?

Answer 1

We want to determine the final population of the city after 13 years.

Given that;

The population grows by 5.25% each year

Initial population of the city is 220,000

Time is 13 years

Using the formula for exponential growth;

$F=P(1+r)^t$

Where;

F= final amount

P = initial amount = 220,000

r = rate (in decimal) = 0.0525

t= time = 13

substituting the given values we have;

$\begin{gathered} F=220,000(1+0.0525)^{13} \\ F=220,000(1.0525)^{13} \\ F=220,000(1.944855586) \\ F=427,868.2289 \\ F\approx427,868 \end{gathered}$

Therefore, the final population of the city after 13 years is 427,868 people