Exponential growth

Question

During a research experiment, it was found that the number of bacteria in a culture grew at a rate proportional to its size. At 9 am there were 2,000 bacteria present in the culture. At noon, the number of bacteria grew to 2,800. How many bacteria will there be at midnight?

Answer 1

Over a period of 3 hours (9:00-12:00) it grew by a factor of 2800/2000 = 1.4, starting at 2000.  Then the population obeys

 

P(t) = 2000 (1.4)^t/3

 

where t = number of hours elapsed since the time the population was 2000.  At midnight, it will be 15 hours past that time.

 

P(15) = 2000 (1.4)^15/3 ≅ 10,756

 

 

Answer 2

Yes, what Arturo claims!