Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. A sample of 1800 bacteria selected from this population reached the size of 2272 bacteria in five hours. Find the hourly growth parameter.

Question

Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model.  A sample of 1800 bacteria selected from this population reached the size of 2272 bacteria in five hours. Find the hourly growth parameter.

Reiny · Answer

so number = a e^(kt) 2272 = 1800 e^(5k) 1.26222... = e^5k ln 1.26222... = 5k k = .04657.. <----- your hourly growth parameter the instantaneous rate of growth is appr 4.657% per hour.