Answer
$f$ exponential
$g$ neither linear, nor exponential
$h$ exponential
Work Step by Step
For $f(x)$:
A function is linear if the slope is a constant.
$$\begin{aligned} &m= \frac{85.9-95.4}{5-0}=-1.9 \\ & m= \frac{77.3-85.9}{10-5}=-1.72\end{aligned}$$
The function is not linear.
We check if ratios of consecutive values are constant to see if it is exponential:
$$
\begin{aligned}
\frac{85.9}{95.4}\approx 0.900\\
\frac{77.3}{85.9}\approx 0.900\\
\frac{69.6}{77.3}\approx 0.900\\
\frac{62.6}{69.6}\approx 0.900
\end{aligned}
$$ Hence: the function $f$ is exponential.
For $g(x)$:
We check if $g$ is linear.
$$\begin{aligned} &m= \frac{40.9-44.8}{5-0}=-0.78 \\ & m= \frac{36.8-40.9}{10-5}=-0.82\end{aligned}$$
The function is not linear.
We check if the function $g$ is exponential:
$$
\begin{aligned}
\frac{40.9}{44.8}\approx 0.913\\
\frac{36.8}{40.9}\approx 0.900\\
\frac{32.5}{36.8}\approx 0.883
\end{aligned}
$$ Hence: the function $g$ is not exponential.
For $h(x)$:
We check if $h$ is linear.
$$\begin{aligned} &m= \frac{36.6-37.3}{5-0}=-0.14 \\ & m= \frac{35.9-36.6}{10-5}=-0.14\\ & m= \frac{35.2-35.9}{15-10}=-0.14 \frac{34.5-35.2}{20-15}=-0.14.
\end{aligned}$$
The function is linear.
We check if the function $h$ is exponential:
$$
\begin{aligned}
\frac{40.9}{44.8}\approx 0.913\\
\frac{36.8}{40.9}\approx 0.900\\
\frac{32.5}{36.8}\approx 0.883
\end{aligned}
$$ Hence: the function $g$ is not exponential.
