Problem $1$ The data for time vs flow rate is obtained from a system where the fluid flows in the positive directions and there is no backflow.

$1)$ Compute the flow rate at every second from $0$ to $90$ seconds $(t=0,1,2,..,90)$ using 'spline' method

$2)$ Plot the original data and the interpolated data using spline method

$3)$ Explain the flow rate observed between time $20$ to $30$ seconds. does that the interpolated data makes senses$?$ If not, explain why?

$4)$ Now, compute the flow rate at every second from $0$ to $90$ seconds $(t=0,1,2,$dots.$\mathrm{.}90$ using 'pchip' method

$5)$ In the plot generates in $2)$ add the interpolated data from pchip method

$6)$ Compare the interpolated data between $t=20-35s$ using spline and pchip method.