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The population of a bacteria culture doubles every 2

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The population of a bacteria culture doubles every 2 [#permalink] New post 24 Aug 2006, 03:28
The population of a bacteria culture doubles every 2 minutes. Approx how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria?

The OE from the OG 11 suggests making a chart and doing the straightforward math. Takes way toooo long...

Anybody know a shortcut?
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Re: OG 11 Doubling Shortcuts? [#permalink] New post 24 Aug 2006, 03:34
GMATT73 wrote:
The population of a bacteria culture doubles every 2 minutes. Approx how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria?

The OE from the OG 11 suggests making a chart and doing the straightforward math. Takes way toooo long...

Anybody know a shortcut?


P= 1000*2^(t/2) where t is the time elapsed in minutes

For P=500,000, 2^(t/2)=500

But 2^9=512, approx. 500, so t/2 is approx 9

Thus there will be appoximately 500,000 bacteria in 18 minutes
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Re: OG 11 Doubling Shortcuts? [#permalink] New post 24 Aug 2006, 03:46
kevincan wrote:
GMATT73 wrote:
The population of a bacteria culture doubles every 2 minutes. Approx how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria?

The OE from the OG 11 suggests making a chart and doing the straightforward math. Takes way toooo long...

Anybody know a shortcut?


P= 1000*2^(t/2) where t is the time elapsed in minutes

For P=500,000, 2^(t/2)=500

But 2^9=512, approx. 500, so t/2 is approx 9

Thus there will be appoximately 500,000 bacteria in 18 minutes


Thanx Kevin. Probably helps to have 2^0~2^20 memorized for handy calculations like this.
Re: OG 11 Doubling Shortcuts?   [#permalink] 24 Aug 2006, 03:46
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