please help help help, statistics?

Question

The population of Tanzania in 1995 was about 28.5 million, with an annual growth rate of 3.0 (model: P = 28.5(1.03)^n)

Predict when the population will reach 30 million.

please explain as you're solving. thank you very much

Answer 1

Substitute 30 for P and solve:
30 = 28.5(1.03)^n)
(1.03)^n = 30/28.5
log((1.03)^n) = log(30/28.5)
nlog(1.03) = log(30/28.5)
n = (log(30/28.5))/log(1.03)
n = (log(1.052632))/log(1.03)
Using natural logarithms,
n = 0.05129329 / 0.02955880
n ≈ 1.735297 ≈ 1.74 years