You are operating the fed$-$batch reactor for In Class $8$ to create a starter culture to manufacture Swiss cheese using Lactobacillus casi. Your client is becoming impatient; they want more cheese, now! You decide to shift to exponential feed.

Using the same growth parameters as In Class $8$: YX$/$S $=0\mathrm{.}23$ g X $($g S$)-1,$ KS $=0\mathrm{.}15$ g$/$L$,\backslash$mu max $=0\mathrm{.}7$ h$-1,$ kd $=0\mathrm{.}03$ h$-1$:

If the initial culture volume was $1000$ L$*,$ what is the volume after $2\mathrm{.}6$ hours, in L$,$ if you choose an exponent $($power$)$ equal to the maximum growth rate? Assume that you start from the original feed flow of $4000$ L$/$h and are under isothermal conditions. Under the same conditions, what is the specific growth rate after $3\mathrm{.}9$ hours?What is the cell doubling time after $2\mathrm{.}6$ hours in hours?