exponential growth model

Question

Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. A sample of 2100 bacteria selected from this population reached the size of
2459 bacteria in five hours. Find the hourly growth rate parameter. Note: This is a continuous exponential growth model.

Write your answer as a percentage. Do not round any intermediate computations, and round your percentage to the nearest hundredth.

Answer 1

Let A(t) = number of bacteria in t hours

 

Then, A(t) = 2100e^kt, and A(5) = 2459

 

So, 2100e^5k = 2459

 

              e^5k = 1.1709524

 

                5k = ln(1.1709524)

 

                  k = 0.1578174 ≈ 15.8%