Answer:
187,298.
Explanation:
The equation that model the growth in the city is an exponential function with the form:
[tex]P=P_0\cdot(1+r)^t[/tex]Where P0 is the initial population, r is the growth rate and t is the number of quarters because the rate applies four times per year.
So, replacing P0 by 100,000, r by 4%, and t by 16 quarter ( 4 years x 4 quarters), we get:
[tex]\begin{gathered} P=100000\cdot(1+0.04)^{16} \\ P=100000\cdot1.8729_{} \\ P=187,298.1246 \end{gathered}[/tex]Therefore, after 4 years, the population of the city will be 187,298.
