Question

A cell of some bacteria divides into two cells every 40 minutes.The initial population is 6 bacteria. (a) Find the size of the population after t hours

Answer 1

y(t)=Ae^(rt), at t=0,y=6, since it doubled r=2, means y=12 then
12=6e^(40r)
2=e^(40r) take ln on both sides gives
ln 2=lne^(40r)
ln 2=40r
r=ln2/40=0.017 therefore
y(t)=6e^(0.017t) ...ans