A bacteria culture initially contains 2000 bacteria and doubles every half hour.

Question

A bacteria culture initially contains 2000 bacteria and doubles every half hour.

Find the size of the baterial population after 40 minutes.   

Find the size of the baterial population after 7 hours.

Answer 1

This is an exponential growth problem. There are several ways to solve this problem, here is one way, since we are given doubling times it's easy to consider the growth as a factor of 2 rather than using the exponential function. If N(t) = the amount of something "N" at time "t", then N(t) = No * 2^(a*t) where a is the exponential growth factor and No is the amount you have at time zero. For this example, the known is the time interval of 30 minutes and we know N(30) = 2*No. Now we find "a" by solving for it: "N" doubles every 30 minutes, so, N(30) = 2, No = 1, and 2 = 1 * 2^{(a*30 minutes)}, and solving for "a" we have a = 1/30. Thus, No = 2000 bacteria, a = 1/30 minutes, and you can change t to equal the times given and you have your answer.

Answer 2