Code what you can in python and handwrite the appropriate steps from the question. Problem $17$

$17.$ The table shows the drag coefficient $\backslash ($ c$\_\{$D$\}\backslash )$ of a sphere as a function of Reynold's number $\backslash ($ R e$\{\}^\{3\}\backslash )$ Use a natural cubic spline to find $\backslash ($ c$\_\{$D$\}\backslash )$ at $\backslash ($ R e$=5,50,500\backslash ),$ and $5,000.$ Hint: Use a log$-$log scale.

Comments and modifications for problem $17$:

$-$ Use a base $10$ log$-$log or a natural log scale, but indicate which you are using.

$-$ Fit the spline in the log$-$log space. That is$,$ take the log of the Reynold's number and drag coefficient data to create a data set in the log$-$log space. Then use these new values to create the spline and polynomial fits.

$-$ Obtain two curve fits

$-$ Natural cubic spline

Calculate $($by hand$)$ the first three equations that are to be solved to obtain the cubic spline.

$-$ Polynomial interpolation $($You can use a function written for an earlier assignment.$)$

Plot the data points and the two fits of the data on a log$-$log plot.