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by karthikpandian19 » Sat Jul 07, 2012 8:07 pm
A small town's population doubles every 5 years. Approximately how many years will it take for the population to grow from 100 to 25,000 people?
(A) 15 (B) 20 (C) 30 (D) 35 (E) 40
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by Anurag@Gurome » Sat Jul 07, 2012 8:16 pm
karthikpandian19 wrote:A small town's population doubles every 5 years. Approximately how many years will it take for the population to grow from 100 to 25,000 people?
Algebraic Approach:
Let us assume that it will take 5n years for the population to grow from 100 to 25,000 people.

Population now = 100
Population after 5n years = (2^n)*100

So, (2^n)*100 = 25000
--> 2^n = 250 ≈ 256 = 2^8
--> n = 8

Hence, the correct answer is E.
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by alex.gellatly » Sat Jul 07, 2012 11:21 pm
karthikpandian19 wrote:A small town's population doubles every 5 years. Approximately how many years will it take for the population to grow from 100 to 25,000 people?
(A) 15 (B) 20 (C) 30 (D) 35 (E) 40
The algebraic approach obviously works well, however if you can't figure out how to set up an equation like that simply list out the numbers. Listing out the numbers is fairly easy in the problem because it's just multiplied by 2. The population doubles every five years so...

100*2= 200 in 5 years
200*2= 400 in 10 years
400*2= 800 in 15 years
800*2= 1600 in 20 years
1600*2= 3200 in 25 years
3200*2= 6400 in 30 years
6400*2= 12800 in 35 years
12800*2= 25600 in 40 years

That means the population will be 25600 in 40 years which is very close to 25,000 (Remember they just asked for an approximate value)
Hope this helps, let me know.
The Correct Answer is E
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by GMATGuruNY » Sun Jul 08, 2012 3:16 am
karthikpandian19 wrote:A small town's population doubles every 5 years. Approximately how many years will it take for the population to grow from 100 to 25,000 people?
(A) 15 (B) 20 (C) 30 (D) 35 (E) 40
We could use the formula for exponential growth:

Final Amount = Original Amount * (Multiplier)^(Number of changes)

In the problem above:
Final Amount = 25,000
Original Amount = 100
Multiplier = 2 (since the population keeps doubling)
Number of changes = x.

Plugging these values into the formula, we get:
25,000 = 100 * 2^x
2^x = 250.
Since 2^8 = 256, x ≈ 8.

Since the number of changes = 8, and each change takes 5 years, the total number of years = 8*5 = 40.

The correct answer is E.

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