$.$ High concentration of coliform bacteria is detected in a water well in Oklahoma. Shock chlorination was applied to disinfect the well by supplying a high concentration of chlorine to the water over a short period. After the disinfection treatment, the concentration of coliform bacteria c$,$ is expected to decrease according to

c $=77$e$-1\mathrm{.}5$t $+20$e$-0\mathrm{.}08$t

Where t is time in hours, and c is the bacteria concentration in ppm$.$ Determine the time required for the bacteria concentration to be reduced to $15$ ppm using the Newton$$s method with an initial guess of t $=6$ and a stopping criterion of $1\%($tol$=0\mathrm{.}01).$ Check your result with fsolve function in Python$$s scipy library.

Can you write a code in jupyter notebook.

Answer$=3\mathrm{.}8$ hours