Question

Bacterial cells grow at a rate proportional to the volume of dividing cells at that moment. If V0 is the volume of dividing cells at any time t . Find the time at which the volume of the cells will
be double its original size.

Answer 1

$\frac{dV}{dt}=kV,\;\;V(0)=V_0$

$V=V_0e^{kt}$

$V=2V_0$

Thus, $2V_0=V_0e^{kt}$

So, $ln2=kt$

$t=\frac{ln2}{k}$