Question

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?

Answer 1

`=3645`

Explanation:

`5times(3)^6`

`=5times729`

`=3645`

Answer 2

`5 xx 3^6 = 3,645`

Explanation:

We could just write this out as `5xx3xx3xx3xx3xx3xx3`

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. `xx3`
after 2 hours have elapsed, multiply by 3 twice. `xx3^2`
after 3 hour have elapsed, multiply by 3 thrice. `" " 3^3`
After 4 hours have elapsed, multiply by 3 , 4 times, or `3^4`

Now we can see that there is a pattern emerging.

Population = `5 xx 3^("number of hours")`

=`5 xx 3^6 = 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.

.

Answer 3

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`=3^1*5`.

After `2` hours, the pop.`=3(3^1*5)=3^2*5`

After `3` hours, the pop.`=3(3^2*5)=3^3*5`.

Clearly, after `6` hours, the pop.`=3^6*5=3645`.

In general, the Population after `h` hours`=5*3^h`.

Enjoy Maths.!