Question

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?

Answer 1

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.