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=3645

Explanation:

5times(3)^65×(3)6

=5times729=5×729

=3645=3645

Aug 21, 2016

5 xx 3^6 = 3,6455×36=3,645

Explanation:

We could just write this out as 5xx3xx3xx3xx3xx3xx35×3×3×3×3×3×3

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. xx3×3
after 2 hours have elapsed, multiply by 3 twice. xx3^2×32
after 3 hour have elapsed, multiply by 3 thrice. " " 3^3 33
After 4 hours have elapsed, multiply by 3 , 4 times, or 3^434

Now we can see that there is a pattern emerging.

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

= 5 xx 3^6 = 3,6455×36=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.

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Aug 21, 2016

The population of Bacteria after 66 hours=3645=3645.

Explanation:

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

As is given, after 11 hour, the population=3^1*5=315.

After 22 hours, the pop.=3(3^1*5)=3^2*5=3(315)=325

After 33 hours, the pop.=3(3^2*5)=3^3*5=3(325)=335.

Clearly, after 66 hours, the pop.=3^6*5=3645=365=3645.

In general, the Population after hh hours=5*3^h=53h.

Enjoy Maths.!