the town's population after 17 years is 44,685
Explanation:decrease = rate = 3% = 0.03
t = 17 years
Present population = a = 75,000
y = population after t years
Exponential growth formula:
[tex]y=a(1+r)^t[/tex]Since the poulation is decreasing, the formula becomes (exponential decay):
[tex]y=a(1-r)^t[/tex]inserting into the formula:
[tex]\begin{gathered} y=75000(1-0.03)^{17} \\ y=75000(0.97)^{17} \end{gathered}[/tex][tex]\begin{gathered} y\text{ = 75000(0.5958)} \\ y\text{ = 44,685} \end{gathered}[/tex]Hence, the town's population after 17 years is 44,685
