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The population of grasshoppers doubles in a particular field

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The population of grasshoppers doubles in a particular field [#permalink]

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The population of grasshoppers doubles in a particular field every year. Approximately how many years will it take the population to grow from 2,000 grasshoppers to 1,000,000 or more?
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Re: The population of grasshoppers doubles in a particular field [#permalink]

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New post 18 Sep 2013, 16:57
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jlgdr wrote:
The population of grasshoppers doubles in a particular field every year. Approximately how many years will it take the population to grow from 2,000 grasshoppers to 1,000,000 or more?


\(2^n*2,000\geq{1,000,000}\) --> \(2^n\geq{500}\) --> \(n=9\) (since 2^9=512).

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Hope it helps.
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Re: The population of grasshoppers doubles in a particular field [#permalink]

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New post 08 Jun 2015, 22:24
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Hi All,

Certain questions on Test Day can be solved rather quickly with "brute force" - you don't need to be a genius and you don't need to have an 'elegant' approach....you just need to put pen to pad and do a bit of basic math.

Here, we're told that the population DOUBLES every year. We're asked APPROXIMATELY how many years it takes to go from 2,000 to 1,000,000+....

Start: 2,000
Yr. 1: 4,000
Yr. 2: 8,000
Yr. 3: 16,000
Yr. 4: 32,000
Yr. 5: 64,000
Yr. 6: 128,000
Yr. 7: 256,000
Yr. 8: 512,000
Yr. 9: 1,024,000

So, approximately 9 years have to pass to get to 1,000,000+.

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Re: The population of grasshoppers doubles in a particular field [#permalink]

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New post 15 Oct 2016, 13:21
Final population growth = S * P ^ (t/l)
S = starting population
P = progression (doubles = 2, triples = 3 etc.)
t/l = total amount of iterations
t = time
I = intervals

1,000,000 = 2,000 * 2 ^ (t years/ 1 year) = > 1,000,000 / 2000 = 2^ t = > 500 = 2^t - which from here t = 9
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Re: The population of grasshoppers doubles in a particular field [#permalink]

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New post 07 Apr 2018, 12:50
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Re: The population of grasshoppers doubles in a particular field   [#permalink] 07 Apr 2018, 12:50
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