Expert: Steve Holleran - 3/13/2008

Question
A certain bacteria will triple in 6 hours. If the final count is 8 times the original count, how much time has passed?  

Answer
Hi Holland,

I'm assuming exponential growth here.

If so, the the equation we want to use is

               P = P(0) * e^(kt)

At t=6, P= 3P(0):

             3P(0) = P(0) * e^(6k)

The P(0)'s cancel and you have:

                 3 = e^(6k)   so 6k = ln 3  

                 and k = ln 3 / 6 = 0.1831

Then the final count is 8P(0):

             8P(0) = P(0) * e^(0.1831t)

Again the P(0)'s cancel, and you have

                 8 = e^(0.1831t)  

so               0.1831t = ln 8  and t = ln 8  / 0.1831 = 11.3569 hr.

I hope this is what you needed.

Steve