Question

The town of Wattle has a population that is decreasing steadily.

It is found that the population is decreasing at a rate of 5.4% per year.
How long will it take for the population to be beneath 45% of what it is now?

Answer 1

After 1 yr P1 = .946 Po

After 2 yrs P = .946 P1 = .946^2 Po

After n yrs P = .946^n Po

.45 = .946^n What is n needed to drop P to .45 P

log .45 = n log .946

n = log .45 / log .946 = -.347 /-.0241 = 14.4 years