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Doubling confusion

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Doubling confusion

by futjim » Wed Jul 07, 2010 6:58 pm
Dear all,

I have a rather stupid yet confusing question to ask about doubling.

In a word problem when the question states that something is doubling every minute or 30 seconds, which one of the following should I be thinking of?

a) 2x
b) x^2

And what about tripling? is it 3x or x^3?

So far, my impulses have been telling me to react to 2x but in some questions x^2 is correct. I'm totally confused and am losing sleep because of this.

Can anyone clarify?

Once again, thanks!
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by Rich@VeritasPrep » Wed Jul 07, 2010 7:03 pm
Hey futjim,

I think I see where the confusion is coming from...

Some questions will say something like "double the value of x", and that translates to 2x.

But let's say you get a problem about a bacteria colony whose population doubles every hour. Let's assume, just for the sake of argument, that you start off with a population of 1, then:

After 1 hour --> 2 bacteria
After 2 hours --> 4 bacteria
After 3 hours --> 8 bacteria
...
After t hours --> 2^t bacteria

Did you mean to write 2^x instead of x^2?
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by futjim » Thu Jul 08, 2010 3:33 pm
Hello raz1024,

Thank you for the reply.

Yes, I did mean to type 2^x.

So just to clarify then:

- If it is a bacteria population problem, the double that the questions refers to is 2^t
- For any other problems the words "double the value of x", "x doubles every 10 years" and so on refers to 2x

Wow, this make sense yet it is confusing at the same time. Essentially, there are 2 standards/rules for the word double in math. How interesting.

Thanks again for your help.
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by Stuart@KaplanGMAT » Thu Jul 08, 2010 3:44 pm
futjim wrote:Hello raz1024,

Thank you for the reply.

Yes, I did mean to type 2^x.

So just to clarify then:

- If it is a bacteria population problem, the double that the questions refers to is 2^t
- For any other problems the words "double the value of x", "x doubles every 10 years" and so on refers to 2x

Wow, this make sense yet it is confusing at the same time. Essentially, there are 2 standards/rules for the word double in math. How interesting.

Thanks again for your help.
Hi,

those are actually two ways of expressing the exact same idea.

If x doubles for 4 time periods, then at the end we'll have:

x * 2 * 2 * 2 *2

Of course, we can write:

2*2*2*2 as 2^4,

so another way to express it would be:

x * 2^4.

The way you wouldn't express it is as:

x^4,

since that's not multiplying by 2 every time period, that's multiplying by x.
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by GMATGuruNY » Thu Jul 08, 2010 7:06 pm
futjim wrote:Dear all,

I have a rather stupid yet confusing question to ask about doubling.

In a word problem when the question states that something is doubling every minute or 30 seconds, which one of the following should I be thinking of?

a) 2x
b) x^2

And what about tripling? is it 3x or x^3?

So far, my impulses have been telling me to react to 2x but in some questions x^2 is correct. I'm totally confused and am losing sleep because of this.

Can anyone clarify?

Once again, thanks!
You might find it helpful to memorize the formula for exponential change:

Final = Original * (multiplier)^(number of changes)

Here's an example:

If you put $10 in the bank, and the amount doubles every year for 3 years, how much will you have at the end of the 3 years?

original = 10
multiplier = 2 (because the amount keeps doubling)
number of changes = 3 (because over 3 years the amount will double 3 times)

So final = 10 * 2^3 = 10 * 8 = 80.

Hope this helps!
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