A batch bioprocess for the production of a recombinant protein exhibits a specific production rate $q_P=$

$4{10}^{-6}g$ product cells $\{$:$h).$ The reactor is seeded with $5{10}^5$ cells $\frac{?}{mL}$ and under the operating conditions, the cells double every $15$ hours. Assuming balanced growth conditions how much time is needed for the product titer to reach $5\frac{g}{L}?$

I saw someone else posted this question but I could not understand the reasoning given by the expert. Could the expert please show calculations and explain what they are doing. Thanks