A town starts with 100 people and grows by 9% per year with x representing the number of years. Which of the following functions model this behavior?

Question

Quizplus · Accepted Answer

The function that models the population growth of the town is an exponential function of the form: P(x) = P0 * (1 + r)^x, where P0 is the initial population, r is the annual growth rate as a decimal, and x is the number of years.

Using the given information, we can plug in the values and simplify to find which function matches the model: 
P0 = 100 (the town starts with 100 people) 
r = 0.09 (the town grows by 9% per year)

Option B can be simplified as: 
P(x) = 100(1 + 0.09)^x = 100(1.09)^x

Therefore, the best choice is B.

A Town Starts with 100 People and Grows by 9