E$.$ A $5000L$ reactor is operating at $0\mathrm{.}9$ perfusion rate with at steady state cell concentration of $1\mathrm{.}2E11$

cells $\frac{?}{mL}$ and a DO set$-$point of $37\mathrm{.}5\%.$ It is desired to determine the mass transfer co$-$efficient

parameter $(k_L-a)$ to evaluate oxygen sparging and fluid mixing. Therefore, the oxygen sparge is stopped

for $5$ minutes and then restarted. Determine the mass transfer co$-$efficient parameter $(\{$:$k_L-a)$ in units of $\frac{L}{s}$

based on the dynamic DO profile below.

YOU DO NOT NEED TO FILL OUT ALL OF THE TARIF TO ARRIVE AT YOUR ANSWER

$($ PLEASE SHOW OR PROVIDE THE FORMULA TO FILL IN THE TABLE$)$