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Word problem- is there a faster way to solve it?

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by \'manpreet singh » Fri Jun 22, 2012 11:09 am
The population of a certain type of bacterium triples every 10 minutes. If the population of a colony 20 minutes ago was 100, in approximately how many minutes from now will the bacteria population reach 24,000?

I need to know a faster and quicker way to solve the problem.
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by Anurag@Gurome » Fri Jun 22, 2012 11:18 am
'manpreet singh wrote:The population of a certain type of bacterium triples every 10 minutes. If the population of a colony 20 minutes ago was 100, in approximately how many minutes from now will the bacteria population reach 24,000?
Refer to the post here for an algebraic approach >> https://www.beatthegmat.com/algebraic-wa ... tml#445859[/b]
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by Anurag@Gurome » Fri Jun 22, 2012 11:22 am
If anyone is fast enough with calculation, (s)he can prefer this method.

The population triples every 10 .

Population 20 minutes ago = 100
Population 10 minutes ago = 300
Population at present = 900
Population 10 minutes later = 2,700
Population 20 minutes ago = 8,100
Population 30 minutes ago = 24,300 ≈ 24,000

Hence, approximately after 30 minutes from now the bacteria population will reach 24,000.
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by GMATGuruNY » Fri Jun 22, 2012 1:34 pm
'manpreet singh wrote:The population of a certain type of bacterium triples every 10 minutes. If the population of a colony 20 minutes ago was 100, in approximately how many minutes from now will the bacteria population reach 24,000?

I need to know a faster and quicker way to solve the problem.
We could use the formula for exponential growth:

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

In the problem above:
Final Amount = 24,000
Original Amount = 100
Multiplier = 3 (since the population keeps tripling)
Number of changes = x.

Plugging these values into the formula, we get:
24,000 = 100 * 3^x
3^x = 240.
Since 3� = 243, x ≈ 5.

Since the number of changes = 5, and each change takes 10 minutes, the total time needed = 5*10 = 50 minutes.
Since the starting time was 20 minutes ago, the population will reach 24,000 about 30 minutes from now.
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by \'manpreet singh » Sat Jun 23, 2012 10:03 am
Thanks Mitch and Anurag.

Mitch i will prefer your method for such kind of problem. :D :) :)
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