Question

In 1995, the population of a town was 33,500. It is decreasing at a rate of 2.5% per decade.

a. Identify whether the function is a growth or decay function.

b. Write the function, f(n), that expresses the population of the town after (n) decades.

c. What is the population in the year 2025 to the nearest hundred?

Answer 1

• See below

Explanation:

• Initial date = 1995
• Initial population = 33500
• Decrease rate = 2.5% per 10 years

a. It is a decay function as number of population is decreasing over time

b. f(n) = 33500*((100 - 2.5)/100)^n = 33500*(0.975)^n

c. In year 2025, n = (2025 - 1995)/10 = 3

f(3) = 33500*(0.975)^3 = 31100 rounded up