Question

The population of a small town is 500 people. Based on growth of the population in past years, it is estimated that after 1 year the population will be 600 people. Similarly, it is estimated that after 2 and 3 years, the population will be 720 and 864 people, respectively. Which function describes the relationship between year and town population.

a. f(x) = 500(1.2)^x
b. f(x) = 500(1.2)^x-1
c. f(x) = 500(0.2)^x-1
d. f(x) = 500(0.2)^x

Answer 1

The relationship between year and town population can be described by the function f(x) = 500(1.2)^x, where x represents the number of years.

Step-by-step explanation:

The relationship between year and town population can be described by the function f(x) = 500(1.2)^x, where x represents the number of years. This function is represented by option A, f(x) = 500(1.2)^x.

Let's verify this function using the given population values:

• For year 1, f(1) = 500(1.2)^1 = 600, which matches the estimated population.
• For year 2, f(2) = 500(1.2)^2 = 720, which matches the estimated population.
• For year 3, f(3) = 500(1.2)^3 = 864, which matches the estimated population.

Therefore, option A correctly describes the relationship between year and town population.