Answer:
6 years
Step-by-step explanation:
we know that
The equation of a exponential growth is equal to
[tex]y=a(1+r)^x[/tex]
where
y ----> is the population
x ---> is the number of years since now
a ---> is the initial value or y-intercept
r ---> is the rate of change
we have
[tex]a=17,000\ people[/tex]
[tex]r=2.5\%=2.5/100=0.025[/tex]
substitute
[tex]y=17,000(1+0.025)^x[/tex]
[tex]y=17,000(1.025)^x[/tex]
For y=19,600
substitute in the exponential equation and solve for x
[tex]19.600=17,000(1.025)^x[/tex]
[tex](19.600/17,000)=(1.025)^x[/tex]
apply log booth sides
[tex]log(19.600/17,000)=log(1.025)^x[/tex]
[tex]log(19.600/17,000)=xlog(1.025)[/tex]
[tex]x=log(19.600/17,000)/log(1.025)=6\ years[/tex]
