Question

A certain number of bacteria are in a petri dish. If the growth rate is 2.7 percent per hour, how many hours will it take the bacteria to double in number?

Answer 1

This is the concept of exponential growth;
the formula for obtaining the number of bacteria at time t in future is:
f(t)=ae^(kt)
where;
f(t)=population in future
a=initial population
k=constant of proportionality.
suppose the initial population was x, when the population doubles it will be 2x at a future time t. 
k=0.027
thus substituting the above in our formula we get:
2x=xe^(0.027t)
solving for t we get:
2=e^(0.027t)
introducing the log function we get:
ln2=0.027t
thus;
t=(ln2)/0.027
=25.67
therefore;
t=25.67 hours