Problem $1(30$ points$).$ A simple, batch fermentation of an aerobic bacterium growing on methanol gave the results shown in the following table. Calculate the following:

a$.$ Maximum growth rate $({}_{\text{m}\text{a}\text{x}})$

b$.$ Yield on substrate $(Y_{\frac{x}{S}})$

c$.$ Mass doubling time $(t_d)$

d$.$ Saturation constant $(K_s)$

e$.$ Specific growth rate $({}_{\text{n}\text{e}\text{t}})$ at $t=10h$

$\backslash$table$[[$Time $(h),x(\frac{g}{l}),S(\frac{g}{l})$