Question

A culture of bacteria doubles every 2 hours. if there are 500 bacteria at the beginning, how many bacteria will there be after 24 hours?

Answer 1

There are 500 bacteria at the beginning and they double every 2 hours. So, if you want to find the number of the bacteria after 2 hours, you must multiply 500 by 2; after 4 hours - multiply 500 by 4; after 6 hours - multiply 500 by 8; etc.
You can write it like this:

`x=500 * 2^{(t)/(2)}`
where x is the number of the bacteria after t hours


`t=24 \\ \\ x=500 * 2^(24)/(2)=500 * 2^(12)=500 * 4096=2048000`

There will be 2,048,000 bacteria after 24 hours.

Answer 2

This question is exponential; the basic formula is
(final amount) = (initial amount) * 2^(total hours ÷ time it takes to double)

So if F = final amount and t = time in hours,

`F=500*2^ (t)/(2)`

and for this one,

`F=500*2^ (24)/(2)`

`F=500*2^1^2`

`F = 2048000`