Answer:
The Population growth function is given by:
\(A(t) = A_0(1+r)^t\)
where
\(A_0\) is the initial population.
r is the growth rate (in decimal)
t is the time in year.
As per the statement:
The population of Augusta, WI, had a population of 1253 in 2000.
In 2000
⇒\(A_0 =1253\)
It is also given that the population increased by 3% each year
⇒r = 3% = 0.03
then;
\(A(t) =1253(1+0.03)^t\) .....[1]
We have to find the population of Augusta in 2016.
⇒t = 16 years
Substitute the given values in [1] we have;
\(A(t) =1253(1+0.03)^{16}\)
⇒\(A(t) =1253(1.03)^{16}\)
⇒\(A(t) =1253 \cdot 1.60470644\)
Simplify:
A(t) = 2,010.69717
Therefore, the population of Augusta in 2016 is, 2,010.7
