# Suppose an experiment begins with 5 bacteria, and the bacteria population triples every hour. What would be the population of the bacteria after 6 hours?

##### 3 Answers

#### Explanation:

#### Explanation:

We could just write this out as

But this method would not be practical if we had to work it out for 24 hours, or for a week. If we can find a pattern or method, we will be able to work out the population for any time period.

Notice what we have done:

after 1 hour has elapsed, multiply by 3 once.

after 2 hours have elapsed, multiply by 3 twice.

after 3 hour have elapsed, multiply by 3 thrice.

After 4 hours have elapsed, multiply by 3 , 4 times, or

Now we can see that there is a pattern emerging.

Population =

=

If we treat this as a GP, note that we are actually looking for the value of the 7th term, because we started with 5, but the growth in the population is only seen AFTER 1 hour, from the 2nd term.

.

The population of Bacteria after

#### Explanation:

In the beginning of the experiment, no. of bacteria

As is given, after

After

After

Clearly, after

In general, the Population after

Enjoy Maths.!