How many bacteria would be present 15 hours after the experiment began if a set of bacteria begins with 20 and doubles every 2 hours?

1 Answer
Dec 7, 2014

The answer is 3811 bacteria.

Using a function to describe exponential growth, we can say that

A = A_@ * e^(k*t), where

A - is the amount we need to find out (in this case, the number of bacteria after 15 hours of growth);
A_@ - the initial number of bacteria;
k - growth rate;
t - time;

We were given t=15 hours and A_@=20 bacteria; however, both k and A need to be determined.

We will determine k by using the fact that the number of bacteria doubles every two hours - this means that after the first 2 hours, we will have 40 bacteria. So,

40 = 20 * e^(k*2), which gives us a k = 0.35.

Therefore, A = 20 * e^(0.35 * 15) = 3811 bacteria.