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
Aug 21, 2016

=3645

Explanation:

5×(3)6

=5×729

=3645

Aug 21, 2016

5×36=3,645

Explanation:

We could just write this out as 5×3×3×3×3×3×3

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. ×3
after 2 hours have elapsed, multiply by 3 twice. ×32
after 3 hour have elapsed, multiply by 3 thrice. 33
After 4 hours have elapsed, multiply by 3 , 4 times, or 34

Now we can see that there is a pattern emerging.

Population = 5×3number of hours

=5×36=3,645

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.

.

Aug 21, 2016

The population of Bacteria after 6 hours=3645.

Explanation:

In the beginning of the experiment, no. of bacteria=5

As is given, after 1 hour, the population=315.

After 2 hours, the pop.=3(315)=325

After 3 hours, the pop.=3(325)=335.

Clearly, after 6 hours, the pop.=365=3645.

In general, the Population after h hours=53h.

Enjoy Maths.!