Thread: please help with this sum

Hi, my son (13) was asked this question in school. If you have one germ and it doubles every 20 mins for 24 hours. how many germs will you have?

My idea is at 20 mins you would have 2 germs then at 40 mins you would have 4 germs then at 60 mins you would have 8 germs at 80 mins you would have 16 germs at 100 mins you would have 32 germs and so on...

Giving that 24 hours has 1440 mins then you would have to continue the string until you reach the 1440 mins

Am i right or wrong? if im wrong how do i figure it out?

I'm going to argue with this one, since it is worded carelessly. My objection will be more clear if we name the germ. Let's call it "Steve" and rephrase.

... If you have one germ named Steve and Steve doubles every 20 mins for 24 hours...

In this case, we get only one (1) new germ every 20 minutes.

hmm that makes more sense, after all its a bit of a strange question to ask a 13 year old, that indeed would make more sense

Your idea is exactly correct.
First figure out how many times the organisms will double in 1440 minutes. There are many ways to figure out how many periods of 20 minutes there are in 1440 minutes: for example, it is the fraction 1440/20 = 144/2 = (12*12)/2 = 12*6 = 72. Or if he's up to it, you can do long division.
So the organism doubles 72 times. The first time, it becomes 2. The second time, it becomes twice the previous time: 2*2. The third time, twice the previous time: $\displaystyle 2\times 2\times 2 = 2^3$, and so on. following this pattern, it is easy to see that on the 72nd period, there will be how many germs?

to be honest i dont have a clue, im not really a mathematical person.

2 to the power 72 = 4,722,366,482,869,645,213,696

This is a weird question for a 13 year old. Oh and like previously stated, it's 2 to the power 72 or 4.722 x 10^21.

Now after re-reading the question I think it is only stating that the original bacteria doubles every 20 minutes. So there would be the original bacteria plus the 72 germs that the original bacteria spawned in the 1440 minute period.

If it was a penny:
$47,223,664,828,696,452,136.96