From the information available, the initial population was 16,007. That figure was taken as at the year zero which is January 1, 2014.
This means
[tex]\begin{gathered} Yr1=2015-2014 \\ Yr2=2016-2014 \\ Yr3=2017-2014 \end{gathered}[/tex]
This trend would be used until we get to January 1, 2030, when we would calculate as follows;
[tex]Yr16=2030-2014[/tex]
Note that the years count from Jan 1 to Jan 1.
The function that models the yearly growth is;
[tex]f(x)=16007(1.031)^x[/tex]
Using the first year, 2014 which is year zero, the result would remain 16,007. That is;
[tex]\begin{gathered} f(0)=16007(1.031)^0 \\ f(0)=16007\times1 \end{gathered}[/tex]
For the 16th year, which is year 2030, we woud now have the following;
[tex]\begin{gathered} f(16)=16007(1.031)^{16} \\ f(16)=16007(1.629816253511204) \\ f(16)=26,088.4687699\ldots \end{gathered}[/tex]
Rounded to the nearest whole number, this figure becomes;
ANSWER:
[tex]\text{Population}\approx26,088[/tex]
