The function f(t) = 24,500(0.84) models the population of a town t years

Question

after 2008. What rate is the population of the town decreasing each year?
A. 16%
B. 24.5%
C. 75.5%
D. 84%

Answer 1

If f(t) = 24,500(0.84) mean f(t) =24,500 ∙ 0.84ᵗ

then:

t = present year

t - 1 = last year

24,500 ∙ 0.84ᵗ = population in present year

24,500 ∙ 0.84ᵗ⁻¹ = population in last year

Rate of decreasing = 1 - ( 24,500 ∙ 0.84ᵗ / 24,500 ∙ 0.84ᵗ⁻¹ ) = 1 - 0.84ᵗ / 0.84ᵗ⁻¹ = 1 - 0.84 = 0.16 = 16%