Answer:
10.4 years
Step-by-step explanation:
Given the population of a small town is initially 13000 and decreasing at the rate of 4% per year, you want to know the number of years it will take for the population to reach 8500.
Exponential decay
The equation for exponential decay is ...
population = (initial population) · (1 - decay rate)^t
Application
Here, the initial population is 13000, the decay rate is 4%, and the population of interest is 8500. This gives an equation we can solve for t.
8500 = 13000 · (1 -0.04)^t
8500/13000 = 0.96^t . . . . . . . divide by 13000
log(17/26) = t·log(0.96) . . . . . take logs
t = log(17/26)/log(0.96) ≈ 10.408
It will take about 10.4 years for the population to reach 8500 people.
