Question

Bacterial cells grow at a rate proportional to the volume of dividing cells at that moment. If 0V 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

dv/dt=kV

V(0)=V₀

V=V₀e^kt

V=2V₀ , from this formula it follows that

2V₀=V₀e^kt

2=e^kt ==> ln2=kt

ANSWER: t=ln2/k.