Answer:
[tex]10.4\ years[/tex]
Step-by-step explanation:
In this problem we have a exponential function of the form
[tex]y=a(b)^{x}[/tex]
where
y is the population of a town
x is the number of years since 2010
a is the initial value
b is the base
[tex]a=72,000\ people[/tex]
[tex]b=1+0.08=1.08[/tex]
substitute
[tex]y=72,000(1.08)^{x}[/tex]
For [tex]y=160,000\ people[/tex]
substitute in the equation and solve for x
[tex]160,000=72,000(1.08)^{x}[/tex]
[tex](160/72)=(1.08)^{x}[/tex]
Apply log both sides
[tex]log(160/72)=(x)log(1.08)[/tex]
[tex]x=log(160/72)/log(1.08)[/tex]
[tex]x=10.4\ years[/tex]
