Bacteria Growth Math Problem

Question

The number of bacteria in a culture is increasing according to the law of exponential growth. After 3 hours there are 100 bacteria, and after 5 hours there are 400 bacteria. How many bacteria will there be after 6 hours?

Answer 1

P = Poe^rt

100 = Poe^3r

400 = Poe^5r

divide

4 = e^2r

ln4 = 2r

r = ln4/2 = about .6931 = 69.31% growth rate

Po = 100/e^3r = 100/8 = 12.5 = original Population

after 6 hours

P = 12.5/e^6r = 12.5(64) = 400 after 6 hours