The snowfall accumulation at Logan Airport $t$ hr after a 33 -hr snowstorm in Boston in 1995 is given in the following table.
$$\begin{array}{l}
\begin{array}{|l|c|c|c|c|c|c|}
\hline \text { Hour } & 0 & 3 & 6 & 9 & 12 & 15 \\
\hline \text { Inches } & 0.1 & 0.4 & 3.6 & 6.5 & 9.1 & 14.4 \\
\hline
\end{array}\\
\begin{array}{|l|c|c|c|c|c|c|}
\hline \text { Hour } & 18 & 21 & 24 & 27 & 30 & 33 \\
\hline \text { Inches } & 19.5 & 22 & 23.6 & 24.8 & 26.6 & 27 \\
\hline
\end{array}
\end{array}$$
By using the logistic curve-fitting capability of a graphing calculator, it can be verified that a regression model for this data is given by
$$ f(t)=\frac{26.71}{1+31.74 e^{-0.24 t}}$$
where $t$ is measured in hours, $t=0$ corresponds to noon of February 6, and $f(t)$ is measured in inches.
a. Plot the scatter diagram and the graph of the function $f$ using the viewing window $[0,36] \times[0,30]$.
b. How fast was the snowfall accumulating at midnight on February $6 ?$ At noon on February $7 ?$
c. At what time during the storm was the snowfall accumulating at the greatest rate? What was the rate of accumulation?