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Hope this helps.
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n - number of 2 hours from now to cross 250000

so 2^(n+2)(1000) = 250000
now n must be integer as the possible answer are all integer
2^(n+2) = 256 (nearest 2 factor)
n+ 2 = 8
n = 6
total hours = 12 answer is D

Is there a formula I could apply?

Yes there is formula you can apply but be careful while using it.

This question is a very simple application of Geometric progression wherein b/a = c/b = r i.e. the ratio of any two consecutive terms in a series is always constant.
Series in this question is 1 ,2 , 4,8,16,32........250
Nth term of GP is given by = (first term) ((Ratio^n)-1)

So the question is what is the Least value of n so that
250 < (first term) ((Ratio^n)-1)

I am leaving the remaining part so that others can apply this concept on their own.

In case, anyone didn't get the solution, let me know

Hi,

You can refer to gurpreetsingh's post. He has used the same concept, though he has reduced the no of terms.

The confusion comes from the interpretation of the formula:
\(a_1\) is the first term and then \(a_n=a_1R^{n-1}\), which is the term on the \(n\)th place. Between the first term and the \(n\)th term, \(n-1\) multiplications by the ratio \(R\) take place, and this is reflected in the exponent of \(n-1\).

Using the formula, you deduced that if \(a_1=4000\) is the first term, then the 7th term will be greater than 250,000. Between the first population and the 7th one, 6 cycles of 2 hours passed, a total of 12 hours, which is the correct answer.
According to the question, your answer should be \(n-1\) from your formula and not \(n\).
In other posts, \(2^n\) was considered, which means \(n\) represents the number of multiplications by \(n\), and obviously the \((n+1)\)th term is greater than 250,000. In both cases we talk about 6 and 7, the difference is whether you called 6 \(n\) or \(n-1\).
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4 hours ago: 1,000
2 hours ago: 2,000
Now: 4,000
In 2 hours: 8,000
in 4 hours: 16,000
in 6 hours: 32,000
in 8 hours: 64,000
in 10 hours: 128,000
in 12 hours: 256,000

I also did the same as fourteenstix, starting with adding a time for now and leaving it blank. The stem says that it doubles every 2 hours. We know that 4 hours ago their number was 1000. So, we add - 4 hours and the number 1000. In 2 hours, their number doubles, so we add - 2 hours and the number 2000. Using the same logic, their number is now 2000*2= 4000. We continue by adding hours to now, so now+2, now+4, now+6..... When we reach to + 12 their number is 256000, which is more than 250000, and we cn stop!

- 4 hours: 1,000
-2 hours: 2,000
Now: 4,000
+ 2 hours: 8,000
+ 4 hours: 16,000
+ 6 hours: 32,000
+ 8 hours: 64,000
+ 10 hours: 128,000
+ 12 hours: 256,000

i am bit confused with this topic can anyone explain the theory behind this problem.
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Hi AkshayDavid

The formulae you specified can be used if percentage is used.
In this sum r = 100
The correct formulae that can be used here is final pop = initial pop ( 1 + rn/100)^(t/n)

There rn is % change in n period
n is the period when compounding happens

Rn = 100
n = 2
T is. What is asked for