Question

Population in a Small Town, USA was 5,054 in 2007. The populations increase by 2% annually. Show and explain all work.

Answer 1

Answer: a. $f(x)=5054(1.02)^x$

b. The population in 2032 will be 8292.

Step-by-step explanation:

Exponential growth equation: $y=a(1+r)^x$, where a = initial value , r = growth rate, x = time period

Given: a = 5054 , r= 0.02

a. Required exponential growth function: $f(x)=5054(1+0.02)^x$

$f(x)=5054(1.02)^x$

b. For 2032, x= 25

$f(25)=5054(1.02)^{25}$

$\approx8291.62\approx8292$

The population in 2032 will be 8292.