A batch bioprocess for the production of a recombinant protein exhibits a specific production rate qP $=4$x$10-6$ g product$/(106$ cells $.$ h$).$ The reactor is seeded with $5$x$105$ cells$/$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 $5$ g$/$L$?.$ Please show calculations