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A certain bacteria colony doubles in size every day for 20 [#permalink]
 12 Dec 2012, 13:42
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A certain bacteria colony doubles in size every day for 20 days, at which point it reaches the limit of its habitat and can no longer grow. If two bacteria colonies start growing simultaneously, how many days will it take them to reach the habitat’s limit? A. 6.33 B. 7.5 C. 10 D. 15 E. 19
Last edited by Bunuel on 13 Dec 2012, 02:50, edited 1 time in total.
Renamed the topic and edited the question.
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A certain bacteria colony doubles in size every day for 20 days, [#permalink]
12 Dec 2012, 13:55
samsonfred76 wrote: simultaneous grow = same amount of time
In 20 days we should expect to have P(2)^20
So if we have two things doing the job of getting us there then;
2^x + 2^x = 20
2(2)^x=2
2^(x+1)=2^20
x+1 = 20
x = 19
We do not need additional information to answer this.
More often than not, if you start thinking the question is wrong chances are you are wrong! If the colony doubles every day then on 20th day the size should be P 2^19 and not P 2^20..right ?
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Re: A certain bacteria colony doubles in size every day for 20 [#permalink]
12 Dec 2012, 15:09
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Let the size at the colony at the start of 20 days be = 1
At the end of the first day it would be 2...At the end of the second day it would be 2(2) and the day after that (2)(2)(2)...You can see then that following the same pattern at the end of 20 days you have (2)^20 since the population doubles...
Hope this helps...
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Re: A certain bacteria colony doubles in size every day [#permalink]
12 Dec 2012, 21:10
Let a be the number of bacteria in the colony at start of day 1. a * 2^(20) = 2a * 2^(x) => x = 20 -1 = 19 Option E
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Re: A certain bacteria colony doubles in size every day [#permalink]
12 Dec 2012, 21:17
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gmatgeek wrote: A certain bacteria colony doubles in size every day
for 20 days, at which point it reaches the limit of its
habitat and can no longer grow. If two bacteria
colonies start growing simultaneously, how many
days will it take them to reach the habitat’s limit?
6.33
7.5
10
15
19 Say the colony has x bacteria in the beginning. 1st day - 2x bacteria 2nd day - 2^2x bacteria 3rd day - 2^3x bacteria . 20th day - 2^{20}x bacteria If we start with 2 bacteria colonies, it means there are already 2x bacteria (equal to number of bacteria at the end of the first day in the first case). In how many more days will they reach 2^{20}x ? Another 19 days!
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Re: A certain bacteria colony doubles in size every day [#permalink]
12 Dec 2012, 21:24
Minimal math answer.
If the bacteria doubles its size everyday and takes 20 days to fill up its habitat, then the previous day it filled up half the habitat.
So if it takes 1 bacteria 19 days to fill up half its habitat, it takes 2 bacteria 19 days to fill up the habitat.
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Re: A certain bacteria colony doubles in size every day for 20 [#permalink]
13 Dec 2012, 02:58
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Re: A certain bacteria colony doubles in size every day for 20 [#permalink]
15 Dec 2012, 06:34
I am not sure whether ny nethod works for everybody but this is how i did. So let say our limit is 5 days (just for easiness of calculation) and we have one collony with 1 bacterium in the first day, so in 5 days we have 1+2+4+8+16=31 bacteria, but if we have two colonies, then in order to fill the max capacity of 31 bacteria we need overall 4 days (1+2+4+8=15 and 1+2+4+8=15). The same principle applies for 20 days, then we need 19 days to fill the max capacity with two colonies. E is the answer. Hope thats helpful!
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Re: A certain bacteria colony doubles in size every day for 20 [#permalink]
16 Dec 2012, 04:21
Ans: If there is one bacteria colony, then it will reach the limit of its habitat in 20 days which is 2^19 If there are two bacteria colonies growing simultaneously, then they would multiply as 2, 2^2, 2^3 in order to reach the limit of habitat they would need one day less than normal which is 19 days. (E).
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Re: A certain bacteria colony doubles in size every day for 20 [#permalink]
16 Dec 2012, 18:24
Two colonies double every day, the given limit value is 2^20 (the asked growth, x - number of days (doublings)): 2(2^x)=2^20 Manipulate the exponent: 2^(x+1)=2^20 Solve for x: x=19 The answer is E.
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Re: A certain bacteria colony doubles in size every day for 20
[#permalink]
16 Dec 2012, 18:24
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