Question

The population of a small town is 40,740. It's population falls by 8% per year. How many years later will the population be 14,550? (Assume that the growth rate is annualized and use the formula for compound growth: A = P ( 1 + r n ) n t . If the compounding frequency is not given, use n = 1 .)

Answer 1

Answer:

0.9101523758 ≈ 1 year

Step-by-step explanation:

The population of a small town is 40,740.

Its population falls by 8% per year.

Given: Compound interest Amount (A) = P( 1 + $\frac{r}{n}$$)^{nt}$

14,550 = 40,740(1 + $\frac{-8}{100 * 1}$$)^{t*1}$

14,550 = (40,740 - 3259.2$)^{t}$

14,550 = (37,480.8$)^{t}$

t * log 37,480.8 = log 14,550

t = $\frac{ log 14,550}{log 37,480.8}$ = 0.9101523758 ≈ 1 year