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# The population of a bacteria colony doubles every day. If it was start

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The population of a bacteria colony doubles every day. If it was start  [#permalink]

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Updated on: 17 Feb 2015, 08:35
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The population of a bacteria colony doubles every day. If it was started 9 days ago with 2 bacteria and each bacteria lives for 12 days, how large is the colony today?

A. 512
B. 768
C. 1024
D. 2048
E. 4096

My wrong think:

If we have 2 bacteria in first day than it will 2 bacteria in first day. In second day 2*2 or 2^2, so if ^2=2 days than 9 days will be ^9. So my answer is 2^9 or 512.

Help to undestand why we shoul take 2*2^9.

Thanks

M06-18

Originally posted by WishMasterUA on 04 Jun 2011, 02:53.
Last edited by Bunuel on 17 Feb 2015, 08:35, edited 1 time in total.
Renamed the topic and edited the question.
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Re: The population of a bacteria colony doubles every day. If it was start  [#permalink]

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04 Jun 2011, 09:12
2
thought about it and i think when you say 9 days ago means today is 10th day.
so it should be 2^10

think of this as in real life we say i gave exam 7 days (last saturday) so today is 8th day.
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Re: The population of a bacteria colony doubles every day. If it was start  [#permalink]

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04 Jun 2011, 09:19
WishMasterUA wrote:
If we have 2 bacteria in first day than it will 2 bacteria in first day. In second day 2*2 or 2^2, so if ^2=2 days than 9 days will be ^9. So my answer is 2^9 or 512.

Help to undestand why we shoul take 2*2^9.

Thanks

Me think of this as follows- as mentioned 9 days ago 2 bacteria was present i.e. 2^1 (and since it was 9 days ago that means we are standing at 10 the today)

so first day we have popn as 2^1, second day 2^2, third day 2^3 ....and so on ...

so at the 10the day (present) we will have 2^10 popn.

Hope it helps!
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Re: The population of a bacteria colony doubles every day. If it was start  [#permalink]

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04 Jun 2011, 09:22
on the first day it was started with 2.

at start count = 2 day 1
at the start of day 2, count = 2*2
=> at the start of nth day, count = 2*2^n-1

here n = 10...as pointed by agdimple333.
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Re: The population of a bacteria colony doubles every day. If it was start  [#permalink]

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04 Jun 2011, 09:30
gurpreetsingh wrote:
on the first day it was started with 2.

at start count = 2 day 1
at the start of day 2, count = 2*2
=> at the start of nth day, count = 2*2^n-1

here n = 10...as pointed by agdimple333.

Well i think Q stem itself says that at the start of the 1st day we have 2^1 popn so at the sart of the 10th day also we shall have 2^10
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Re: The population of a bacteria colony doubles every day. If it was start  [#permalink]

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04 Jun 2011, 09:35
2
WishMasterUA wrote:
Population of a bacteria colony doubles every day. If it was started 9 days ago when 2 bacteria were born in a deserted colony and each bacteria lives for 12 days, how large is the colony today?

1) 512
2) 768
3) 1024
4) 2048
5) 4096

My wrong think:

If we have 2 bacteria in first day than it will 2 bacteria in first day. In second day 2*2 or 2^2, so if ^2=2 days than 9 days will be ^9. So my answer is 2^9 or 512.

Help to undestand why we shoul take 2*2^9.

Thanks

9 days ago- 2
8 days ago- 4
7 days ago- 8
6 days ago- 16
5 days ago- 32
4 days ago- 64
3 days ago- 128
2 days ago- 256
Yesterday- 512
Today- 1024

Ans: "C"
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Re: The population of a bacteria colony doubles every day. If it was start  [#permalink]

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04 Jun 2011, 09:40
fluke wrote:
WishMasterUA wrote:
Population of a bacteria colony doubles every day. If it was started 9 days ago when 2 bacteria were born in a deserted colony and each bacteria lives for 12 days, how large is the colony today?

1) 512
2) 768
3) 1024
4) 2048
5) 4096

My wrong think:

If we have 2 bacteria in first day than it will 2 bacteria in first day. In second day 2*2 or 2^2, so if ^2=2 days than 9 days will be ^9. So my answer is 2^9 or 512.

Help to undestand why we shoul take 2*2^9.

Thanks

9 days ago- 2
8 days ago- 4
7 days ago- 8
6 days ago- 16
5 days ago- 32
4 days ago- 64
3 days ago- 128
2 days ago- 256
Yesterday- 512
Today- 1024

Ans: "C"

Awe nice detailed one fluke !!
I guess catch here was at the start of the day you have 2 B then afterwards multiply by 2 daily..
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Re: The population of a bacteria colony doubles every day. If it was start  [#permalink]

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04 Jun 2011, 09:46
yogesh1984 wrote:
fluke wrote:
WishMasterUA wrote:
Population of a bacteria colony doubles every day. If it was started 9 days ago when 2 bacteria were born in a deserted colony and each bacteria lives for 12 days, how large is the colony today?

1) 512
2) 768
3) 1024
4) 2048
5) 4096

My wrong think:

If we have 2 bacteria in first day than it will 2 bacteria in first day. In second day 2*2 or 2^2, so if ^2=2 days than 9 days will be ^9. So my answer is 2^9 or 512.

Help to undestand why we shoul take 2*2^9.

Thanks

9 days ago- 2
8 days ago- 4
7 days ago- 8
6 days ago- 16
5 days ago- 32
4 days ago- 64
3 days ago- 128
2 days ago- 256
Yesterday- 512
Today- 1024

Ans: "C"

Awe nice detailed one fluke !!
I guess catch here was at the start of the day you have 2 B then afterwards multiply by 2 daily..

Thanks great detail
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Re: The population of a bacteria colony doubles every day. If it was start  [#permalink]

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04 Jun 2011, 09:48
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Joined: 08 Sep 2010
Posts: 129
Re: The population of a bacteria colony doubles every day. If it was start  [#permalink]

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11 Jun 2011, 18:07
fluke wrote:
WishMasterUA wrote:
Population of a bacteria colony doubles every day. If it was started 9 days ago when 2 bacteria were born in a deserted colony and each bacteria lives for 12 days, how large is the colony today?

1) 512
2) 768
3) 1024
4) 2048
5) 4096

My wrong think:

If we have 2 bacteria in first day than it will 2 bacteria in first day. In second day 2*2 or 2^2, so if ^2=2 days than 9 days will be ^9. So my answer is 2^9 or 512.

Help to undestand why we shoul take 2*2^9.

Thanks

9 days ago- 2
8 days ago- 4
7 days ago- 8
6 days ago- 16
5 days ago- 32
4 days ago- 64
3 days ago- 128
2 days ago- 256
Yesterday- 512
Today- 1024

Ans: "C"

Good explanation fluke
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Re: The population of a bacteria colony doubles every day. If it was start  [#permalink]

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30 Oct 2011, 14:08
The population of a bacteria colony doubles every day.

How do we know whether the population of bacteria doubled or not on the first day? i.e Population on first day is 2 or 2*2=4?

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Re: The population of a bacteria colony doubles every day. If it was start  [#permalink]

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31 Oct 2011, 04:42
agarwalmanoj2000 wrote:
The population of a bacteria colony doubles every day.

How do we know whether the population of bacteria doubled or not on the first day? i.e Population on first day is 2 or 2*2=4?

There is no mentioned of the count on the "first" day. We are told that 9 days ago, the population started with 2 bacteria and every day hence it doubled
9 days ago count = 2*2^n. n is an integer that goes from 0 to 9
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Re: The population of a bacteria colony doubles every day. If it was start  [#permalink]

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31 Oct 2011, 09:51
1
Ten days in total

2^10
1024
C

Posted from my mobile device
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Re: The population of a bacteria colony doubles every day. If it was start  [#permalink]

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17 Feb 2015, 06:07
What would be the answer if it was 20 days ago?
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Re: The population of a bacteria colony doubles every day. If it was start  [#permalink]

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17 Feb 2015, 06:38
Salvetor wrote:
What would be the answer if it was 20 days ago?

hi salvetor,

the population today should be 2^21, incase there is no restriction in life period..
but here the bacterias life is 12 days..
so only ones born 12 days ago would be alive...
12 days ago the number was 2^9..
therefore todays strength will be 2^21-2^9= 2^9(2^12-1)...
2^9(2^6-1)(2^6+1)
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Re: The population of a bacteria colony doubles every day. If it was start  [#permalink]

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17 Feb 2015, 08:36
WishMasterUA wrote:
The population of a bacteria colony doubles every day. If it was started 9 days ago with 2 bacteria and each bacteria lives for 12 days, how large is the colony today?

A. 512
B. 768
C. 1024
D. 2048
E. 4096

My wrong think:

If we have 2 bacteria in first day than it will 2 bacteria in first day. In second day 2*2 or 2^2, so if ^2=2 days than 9 days will be ^9. So my answer is 2^9 or 512.

Help to undestand why we shoul take 2*2^9.

Thanks

M06-18

We know that the population doubles every day; other information is not really relevant. If the population started ONE day ago (that is yesterday), it would be $$2^2$$ today. If the population started $$N$$ days ago, then today it is $$2^{(N+1)}$$. Today the population size is $$2^{10}$$, which is 1024.

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Re: The population of a bacteria colony doubles every day. If it was start  [#permalink]

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17 Feb 2015, 08:37
Bunuel wrote:
WishMasterUA wrote:
The population of a bacteria colony doubles every day. If it was started 9 days ago with 2 bacteria and each bacteria lives for 12 days, how large is the colony today?

A. 512
B. 768
C. 1024
D. 2048
E. 4096

My wrong think:

If we have 2 bacteria in first day than it will 2 bacteria in first day. In second day 2*2 or 2^2, so if ^2=2 days than 9 days will be ^9. So my answer is 2^9 or 512.

Help to undestand why we shoul take 2*2^9.

Thanks

M06-18

We know that the population doubles every day; other information is not really relevant. If the population started ONE day ago (that is yesterday), it would be $$2^2$$ today. If the population started $$N$$ days ago, then today it is $$2^{(N+1)}$$. Today the population size is $$2^{10}$$, which is 1024.

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Re: The population of a bacteria colony doubles every day. If it was start  [#permalink]

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03 Jun 2016, 05:34
WishMasterUA wrote:
The population of a bacteria colony doubles every day. If it was started 9 days ago with 2 bacteria and each bacteria lives for 12 days, how large is the colony today?

A. 512
B. 768
C. 1024
D. 2048
E. 4096

My wrong think:

If we have 2 bacteria in first day than it will 2 bacteria in first day. In second day 2*2 or 2^2, so if ^2=2 days than 9 days will be ^9. So my answer is 2^9 or 512.

Help to undestand why we shoul take 2*2^9.

Thanks

M06-18

It started 9 days ago. So bacterias keep growing for 9 days+ today= 10 days

2^10= 1024

C is the answer
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Re: The population of a bacteria colony doubles every day. If it was start  [#permalink]

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11 Jul 2018, 03:22
what is the significance of 12 days??

can someone pls explain?
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Re: The population of a bacteria colony doubles every day. If it was start  [#permalink]

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11 Jul 2018, 03:58
Bob2018 wrote:
what is the significance of 12 days??

can someone pls explain?

Hi Bob2018,

Here the question stem is "how large is the colony today" or "how many bacteria are alive today" ?

Given life span of bacteria is 12 days. So, it means that on the 10th day bacteria are alive and we have to determine the no of alive bacteria in the colony.

Cases would be different if restriction of life span is less than 9.
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Re: The population of a bacteria colony doubles every day. If it was start &nbs [#permalink] 11 Jul 2018, 03:58

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# The population of a bacteria colony doubles every day. If it was start

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