Problem
The function $g$ models the anticipated population of an Ohio town in terms of the number of years since 2015 $g(n)=100,000(0.80)^{n}$. By what percentage does this population change each year as the number of years changes from $2015 ?$ $-20 \%$ $-80 \%$ $120 \%$ $20 \%$ $80 \%$
Solution
Step 1 ：The function \(g(n)=100,000(0.80)^{n}\) models the population of the town. The base of the exponent, 0.80, represents the rate of change each year. Since it is less than 1, it indicates a decrease in population each year.
Step 2 ：The percentage change can be calculated as \((1 - 0.80) * 100\%\).
Step 3 ：Final Answer: The population changes by approximately \(\boxed{-20\%}\) each year.
