Question

The current population of Rochester is 211,000 and is decreasing at a rate of 4.1% every ten years. Which function can be used to find the population 30 years from now?

Answer 1

211,000(0.97)t

Explanation:

Firstly; Write the exponential decay function for this situation.

y = a(1 – r)t Write the formula.

= 211,000(1 – 0.041)t Substitute 1700 for a and 0.03 for r.

= 211,000(0.97)t Simplify.

Next; Find the population in function.

y = 1700 Substitute 12 for t.

≈ 1180 Use a calculator and round to the nearest whole number.

The population in 30 years function will be approximately 211,000(0.97)t.