Question

There are some bacteria in a dish. Every hour, each bacterium splits

into 3 bacteria.

Answer 1

(a) At the end of 2 hours, we have 9 bacteria.

(b) At the end of 3 hours, we have 27 bacteria.

Explanation:

The given question is incomplete.

There are some bacteria in a dish. Every hour, each bacterium splits into 3 bacteria.

a) What happens in hours 2 and 3.

b) How many bacteria are there in hours 2 and 3?

Let us assume n = the number of bacteria at a given hour.

Now here given at zero hour, there is only 1 bacteria.

1 bacteria after an hour is split in to 3 bacteria.

So, at the end of 1 hour, we have n(1) = 3

Now, at the end of the second hour, each of the 3 bacteria will split in to 3 more bacteria.

So, n(2) = 3 x 3 = 9 bacteria

So, at the end of 2 hours, we have n(2) = 9

Now, at the end of the third hour, each of the 9 bacteria will split in to 3 more bacteria.

So, n(3) = 9 x 3 = 27 bacteria

So, at the end of 3 hours, we have n(3) = 27

Hence, in total after 3 hours, we have 27 bacteria.