Question

The population of a town t years after the year 2005 can be modeled by the function p(t)=2,020(1.036)ᵗ. Which statement is true?

a. The population of the town is increasing at the rate of 0.6% every year.
b. The population of the town is increasing at the rate of 3.6% every year.
c. The population of the town is increasing at the rate of 0.036% every year.
d. The population of the town is increasing at the rate of 1.036% every year.

Answer 1

The town's population increases at a rate of 3.6% per year, as seen in the model p(t)=2,020(1.036)^t, with 1.036 representing the annual growth rate in decimal form.

Step-by-step explanation:

The population of a town t years after the year 2005 can be modeled by the function p(t)=2,020(1.036)t. To determine the rate at which the population is increasing each year, we look at the number 1.036 in the equation.

This number represents 1 plus the percentage growth rate expressed as a decimal. Since 1.036 can be rewritten as 1 + 0.036, it indicates that the population is growing at a 3.6% rate annually.

Therefore, the correct statement is b. The population of the town is increasing at the rate of 3.6% every year.