Answer:
6 years
Step-by-step explanation:
The initial population of the town here is
[tex]p_0 = 17,000[/tex]
And we know that it grows at a rate of 2.5% each year: this means that after n years, the town's population is given by
[tex]p=(1+\frac{2.5}{100})^np_0[/tex]
Here we want to find the number of years n after which the town population is
p = 19,600
Therefore, we have to re-arrange the equation and solve for n. We get:
[tex]p=1.025^n p_0\\1.025^n = \frac{p}{p_0}\\n=Log_{1.025}(\frac{p}{p_0})=Log_{1.025}(\frac{19600}{17000})=5.76\sim 6[/tex]
So, after approx. 6 years.
