Question

A culture started with 5000 bacteria. After 2 hours, it grew to 5500 bacteria. Predict how many bacteria will be present after 10 hours

Answer 1

The answer is 8000 bacteria after 10 hours.

Answer 2

Initial value:  5000 at time t=0.

B = 5000*e^(k*t)  =>  5500 = 5000*e^(k*2), or  5500 = 5000*(e^k)^2.  Find the growth constant, k:

5500
-------- = 1.1 = e^(2k) = (e^k)^2
5000

Thus, the expo growth equation becomes B = 5000*(1.1)^t

and so, after 10 hrs, the number of bacteria will be B = 5000*(1.1)^10, or
                                                                                 B = 5000*(2.59), or
                                                                                 B = 12969 bacteria