Consider the growth of a microorganism in batch culture. When the substrate concentration

is high, the cell density doubles every $0\mathrm{.}75h,$ the observed substrate yield coefficient is $0\mathrm{.}3$

$gDC\frac{W}{g},$ and substrate consumption is allocated towards biosynthesis $(60\%),$ maintenance

$(10\%),$ as well as product formation $(30\%).$ The product formation is strictly growth

associated. The batch reactor is inoculated with $0\mathrm{.}01gDC\frac{W}{L}$ and $10\frac{g}{L}$ substrate.

Compute the maximum cell density and the time after lag phase required to achieve it$.$