ANSWER
[tex]\text{9 years}[/tex]EXPLANATION
We want to find the number of years that it will take the population to double.
To do this, we have to apply the exponential growth function:
[tex]y=a(1+r)^t[/tex]where y = final value
a = initial value
r = rate of growth
t = time (in years)
For the population to double, it means that the final value must be 2 times the initial value:
[tex]y=2a[/tex]Substitute the given values into the function above:
[tex]\begin{gathered} 2a=a(1+\frac{8}{100})^t \\ \frac{2a}{a}=(1+0.08)^t=1.08^t \\ 2=1.08^t \end{gathered}[/tex]To solve further, convert the function from an exponential function to a logarithmic function as follows:
[tex]\log _{1.08}2=t[/tex]Solve for t:
[tex]\begin{gathered} \frac{\log _{10}2}{\log _{10}1.08}=t \\ \Rightarrow t=9\text{ years} \end{gathered}[/tex]It will take 9 years for the population to double.
