Explanation

Every 3 minutes, the population increases by 20% (which is the same as multiplying by 1.2).

Beginning at 8:54am, this change would occur at 8:57am and again at 9:00am. Use the variable x to represent the original quantity. Note that the 20% increase occurs twice:

x(1.2)(1.2) = 144,000
x = 100,000

Note that you cannot just reduce 144,000 by 20% twice, because 20% is not a percent of 144,000—it is a percent of the unknown, original number.

Alternatively, begin from 144,000 and calculate “backwards”:

From 8:57am to 9:00am: y(1.2) = 144,000, so y =\(\frac{144,000}{1.2}\) = 120,000.

From 8:54am to 8:57am: z(1.2) = 120,000, so z = \(\frac{120,000}{1.2}\)= 100,000.

Total time span : 6 mins. So there will be 2 phases.

Increase rate : 20% in every 3 minutes. That can be expressed as follows :

\((1.2)^2\).

let assume the number of bacteria at the very beginning was x.

x*(1.2)^2= 144000

x = 144000 / 1.44

x = 14400000 / 144

x = 100000.

The best answer is A.

I tried doing a decrease of 20% from 144000 but this method didn't work. Can someone explain why?

If you decrease it by \(20\)%, it means that the value will be \(80\)%.

Let's say a value is 100. Now it increases every day by \(20\)%. So the next day it will be \(120\).

Now if we want to get the value on the first day, while decreasing with your method, it will be \(80\)% of \(120 = \)96

So for the \(20\)% decrease, we have to divide by \(1.20\),a multiplier, to get the correct value.

Please ask if the doubt remains.

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