exponential equation

Question

Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. A sample of 2300 bacteria selected from this population reached the size of 2682 bacteria in four hours. Find the hourly growth rate parameter.

Answer 1

2682 = 2300e^4r

e^4r = 2682/2300 = 1341/1150

4r = ln(1341/1150)

r = ln(1341/1150)/4 = about .0384

= about 3.84% per hour growth rate

A = 2300e^.0384t where t=time measured in hours