Question

A bacteria culture is known to growth at a rate proportional to the amount present.
There are 30 strands of bacteria after 1 hour(s) in the culture; and 150 strands after 4 hours.

Find the differential equation satisfied by the number of bacteria strands, N,
(use the notation k for the positive proportionality factor),
N' =~

Find the growth constant,
k = ~

Find the initial amount of bacteria in the culture,
N_0 = ~

Find the mass of the material N as function of time.