Given:
[tex]\begin{gathered} \text{Number of cities: }C(x)=2.9(1.05)^x \\ \\ \text{Number of people per city: P}(x)=(1.05)^{3x+5} \end{gathered}[/tex]Let's solve for T(x) which represents the approximate population in the region.
To find the approximate population in the region, apply the formula:
[tex]T(x)=C(x)\ast P(x)[/tex]Thus, we have:
[tex]T(x)=2.9(1.05)^x\ast(1.05)^{3x+5}^{}[/tex]Let's solve the equation for T(x).
Thus, we have:
[tex]\begin{gathered} T(x)=2.9((1.05)^{3x+5}(1.05)^x) \\ \\ Apply\text{ power rule:} \\ T(x)=2.9(1.05)^{3x+5+x^{}_{}} \\ \\ T(x)=2.9(1.05)^{3x+x+5} \\ \\ T(x)=2.9(1.05)^{4x+5} \end{gathered}[/tex]Therefore, the function that best describes the approximate population in the region is:
[tex]T(x)=2.9(1.05)^{4x+5}[/tex]ANSWER:
C
[tex]T(x)=2.9(1.05)^{4x+5}[/tex]