Answer
$
g(x)=14.20(0.6024)^x
$
Work Step by Step
We want to find $f(x)=ab^x$,given $g(1.7)=6$ and $g(2.5)=4$. We now find $b$ and $a$.
$$
\begin{aligned}
\frac{a b^{2.5}}{a b^{1.7}} & =\frac{4}{6}=\frac{g(2.5)}{g(1.7)} \\
b^{0.8} & =\frac{4}{6}=\frac{2}{3} \\
b & =\left(\frac{2}{3}\right)^{\frac{1}{0.8}}=\left(\frac{2}{3}\right)^{5/4}\approx 0.6024.
\end{aligned}
$$ and $$
\begin{aligned}
g(1.7) & =a\left(\left(\frac{2}{3}\right)^{5/4}\right)^{1.7}=6 \\
a & =\frac{6}{\left(\frac{2}{3}\right)^{17/8}} \\
& \approx 14.20 .
\end{aligned}
$$ Hence $$
g(x)=14.20(0.6024)^x
$$
