Answer
$
q(x)=82.6446\left(1.03228\right)^x
$
Work Step by Step
Use the ratio method to see if the data can be expressed as an exponential function. We see that
$$
\frac{q(9)}{q(6)}=\frac{q(12)}{q(9)}=\frac{q(18)}{q(9)}=\frac{q(24)}{q(18)}= 1.10
$$
We can now find $b$ and $a$ since the data is exponential.
$$
\begin{aligned}
\frac{a b^9}{a b^6} & =\frac{q(9)}{q(6)} \\
b^3 & =1.10\\
b & =\left(1.10 \right)^{1/3}\approx 1.03228
\end{aligned}
$$ $$
\begin{aligned}
ab^3&=q(3)\\
a \cdot 1.03228^6 & =100 \\
a & =\frac{100}{1.03228^6} \approx 82.6446 .
\end{aligned}
$$ Hence
$$
q(x)=82.6446\left(1.03228\right)^x
$$
