An analyst studying the population of a town determines that the population can be modeled by the formula f(t)=120,000(1.015)t, where f(t) represents the population after years. A city council member makes this claim:


“Based on the formula, after 1 year the population will have increased by 1,800. Since 1,800 divided by 12 is 150, we can use the fact that the population increases by 150 people per month to predict the future population of the town.”
Explain why the city council member’s claim is or is not a valid way to predict the population.
Modify the initial given formula such that it represents the predicted population after months, and use the modified formula to predict the population after 50 months.