Let P=15(1.04)^T give the population (in thousands) of a town, with t in years. If the formula for P is written P=15(b)^t/12, find b exactly.

Question

What is the meaning of b in the context of the population?

Answer 1

P=15(b)^t/12

P/15 = (b)^t/12

log(P/15) = log(b)^t/12

log(P/15) = (t/12)log(b)

(12/t)log(P/15) = log(b)

log(P/15)^12/t = log(b)

(P/15)^12/t = b

For P=15(b)^t/12, 15 is the initial value, Since t is years, then t/12 is in months. That means that b must be the growth rate per month.