Answer = C) (2^6)(10^5)

Initial value \(= 10^5\)

Interval = 10 Minutes

Intervals in 60 Minutes \(= \frac{60}{10} = 6\)

In one hour, value \(= 2^6 * 10^5\)

x bacteria would become 2x in 10 mins, which would become 4x in the next 10 (total 20 mins)...
So in 60 mins x becomes 2^6 times into x

Therefore Answer is C, (2^6)(10^5)

I did this problem by noticing a pattern. Since the population doubles every 10 minutes, basically all we are doing is doubling our coefficient in front of 10^5. It starts out at (1)10^5 and after 10 minutes it is (2)10^5 and at 20 its (4)10^5. I noticed every 10 minutes we are increasing our power of 2.

An hour is 60 minutes, so the bacteria will double 6 times. This means that our coefficient will end up being 2^6. Looking at the answer choices, choice (C), (2^6)(10^5) is correct.

Present population: 10^5
60 mins will have 6 intervals of 10 mins --> so the population will get doubled 6 times in 1hr --> 2*2*2*2*2*2*10^5 -->2^6*10^5

Illustration:
Present - 10^5
after 10 mins - 2*10^5
after 20 mins - 2(2*10^5) = 2^2*10^5
after 30 mins - 2*(2(2*10^5)) = 2^3*10^5
.
.
.
after 60 mins - 2^6*10^5

Ans. C) (2^6)(10^5)
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The correct answer is C.
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Seems like a rip off of this OG10 question by whoever "created" this question :-/

https://gmatclub.com/forum/a-certain-po ... 65536.html
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Hey guys,

How many times does 10 minutes pass in an hour?

60 minutes = 10 minutes * 6

If the number doubles every 10 minutes, that means that it double 6 times in an hour

\(
10^5 * 2 * 2 * 2 * 2 * 2 * 2 \)

What is another way of writing this?

\(10^5 * 2^6\)

The answer is C
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