A bacteria colony increased from 12000 to 18000 in 5 hours. How long will it take for the bacteria to triple?

Question

A bacteria colony increased from 12000 to 18000 in 5 hours. How long will it take for the bacteria to triple?

Answer 1

The answer for this question depends on the model being used to model the growth of the bacteria.  I'm going to assume it's exponential.  So number of bacteria is modeled as A = Se^kt.  A is the amount of bacteria, S is the starting amount of bacteria, k is a growth constant and t is time in hours.  We don't know k so we need to solve for it first and we use the data given above.

 

18000 = 12000*e^5k

 

Solving for k we get:  1.5 = e^5k

                                ln(1.5) = ln(e^5k)

                                ln(1.5) = 5k

                                k = ln(1.5)/5 = .0811

 

Now we can answer the question:

 

36,000 = 12,000e^.0811t

3 = e^.0811t

ln(3) = ln(e^.0811t)

ln(3) = .0811t

t = 13.548 hrs.