The number of bacteria in a certain culture is given by the

The number of bacteria in a certain culture is given by the function B(t)= 10,000e^.05t, where t is time in hours. How long, to the nearest tenth of an hour, will it take the number of bacteria in the culture to double?

Solution

B(t)= 10000 e^(.05t)

Let after t times it becomes double that is 20000

20000=10000e^(.05t)

2=e^(.05t)

taking ln on both sides

ln 2= .05t

t=ln2/.05

t= 13.9 hours