Question

A bacteria culture starts with 100 bacteria and doubles in size every twenty minutes. (a) How many bacteria are there after 3 hours? (b) How many bacteria are there after t hours?

Answer 1

Using the exponential growth formula, there would be 51200 bacteria after 3 hours. The number of bacteria after t hours is represented by the formula N=100*2^(3t).

Step-by-step explanation:

This problem can be solved using the concept of exponential growth. In this case, the number of bacteria doubles every 20 minutes or there is a respective increase every one-third of an hour. Therefore, we have an exponential growth formula: N = N0 * 2^t, where N is the final amount of bacteria, N0 is the initial amount (100 bacteria), and t is the time in the unit of hours/3.

(a) After 3 hours, the time is 3*3=9 in our unit, so N=100*2^9=51200. Thus, there are 51200 bacteria after 3 hours.

(b) After t hours, the time is 3t in our unit. So, the final amount of bacteria, N=100*2^(3t). This represents the number of bacteria after t hours.

Learn more about Exponential Growth