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A colony of bacteria doubles every morning while every

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A colony of bacteria doubles every morning while every [#permalink] New post 19 Dec 2007, 13:42
A colony of bacteria doubles every morning while every evening 1000 bacteria die.

What was the original size of the colony if the colony disappeared by the end of the 3rd day?

What was the original size of the colony if the colony disappeared by the end of the 6th day?

How do i set up an algebraic approach?
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Algebraic expression for colony size [#permalink] New post 19 Dec 2007, 14:44
Looking at the problem, if the initial size is assumed to be N, the size at the end of each day starting from day 1 would be:
N - 1000, 2N - 3000, 4N - 7000, 8N - 15000, 16N - 31000...

Looking at these terms the following formula can be derived to represent the colony size at the end of a given day D.
Size = ((2^D - 1)N - ((2^D)-1) * 1000

Put the size = 0, substitute the value of D and solve for N.

For the given problems, this formula gives the following values:
If colony disappeared by the end of 3rd day then original size = 1750
If colony disappeared by the end of 6th day then original size = 1968.75
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Re: bacteria - algebra [#permalink] New post 19 Dec 2007, 16:17
bmwhype2 wrote:
A colony of bacteria doubles every morning while every evening 1000 bacteria die.

What was the original size of the colony if the colony disappeared by the end of the 3rd day?

What was the original size of the colony if the colony disappeared by the end of the 6th day?

How do i set up an algebraic approach?



1. What was the original size of the colony if the colony disappeared by the end of the 3rd day?

suppose the no of bactaria at the begaining = x
the no of bactaria next morning = 2x
2 {2 (2x - 1000) - 1000} - 1000 = 0
2 (2x - 1000) - 1000 = 1000/2
2x - 1000 = (500 + 1000)/2
x = (750 + 1000)/2
x = 875
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Re: bacteria - algebra [#permalink] New post 19 Dec 2007, 16:23
GMAT TIGER wrote:
bmwhype2 wrote:
A colony of bacteria doubles every morning while every evening 1000 bacteria die.

What was the original size of the colony if the colony disappeared by the end of the 3rd day?

What was the original size of the colony if the colony disappeared by the end of the 6th day?

How do i set up an algebraic approach?



1. What was the original size of the colony if the colony disappeared by the end of the 3rd day?

suppose the no of bactaria at the begaining = x
the no of bactaria next morning = 2x
2 {2 (2x - 1000) - 1000} - 1000 = 0
2 (2x - 1000) - 1000 = 1000/2
2x - 1000 = (500 + 1000)/2
x = (750 + 1000)/2
x = 875


I got 875 too for the first one...
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Re: bacteria - algebra [#permalink] New post 19 Dec 2007, 16:27
GMAT TIGER wrote:
bmwhype2 wrote:
A colony of bacteria doubles every morning while every evening 1000 bacteria die.

What was the original size of the colony if the colony disappeared by the end of the 3rd day?

What was the original size of the colony if the colony disappeared by the end of the 6th day?

How do i set up an algebraic approach?


1. What was the original size of the colony if the colony disappeared by the end of the 3rd day?

suppose the no of bactaria at the begaining = x
the no of bactaria next morning = 2x
2 {2 (2x - 1000) - 1000} - 1000 = 0
2 (2x - 1000) - 1000 = 1000/2
2x - 1000 = (500 + 1000)/2
x = (750 + 1000)/2
x = 875


2. What was the original size of the colony if the colony disappeared by the end of the 6th day?

suppose the no of bactaria at the begaining = x
the no of bactaria next morning = 2x
2{2(2[2 {2 (2x - 1000) - 1000} - 1000] - 1000) - 1000} - 1000 = 0
solving for x, x = 984.375
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 [#permalink] New post 20 Dec 2007, 08:18
I got 875 for the first question. However, if I had this on the GMAT, instead of wasting time trying to write an equation, I'd probably plug in the answers.
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Re: bacteria - algebra [#permalink] New post 20 Dec 2007, 08:37
GMAT TIGER wrote:
GMAT TIGER wrote:
bmwhype2 wrote:
A colony of bacteria doubles every morning while every evening 1000 bacteria die.

What was the original size of the colony if the colony disappeared by the end of the 3rd day?

What was the original size of the colony if the colony disappeared by the end of the 6th day?

How do i set up an algebraic approach?


1. What was the original size of the colony if the colony disappeared by the end of the 3rd day?

suppose the no of bactaria at the begaining = x
the no of bactaria next morning = 2x
2 {2 (2x - 1000) - 1000} - 1000 = 0
2 (2x - 1000) - 1000 = 1000/2
2x - 1000 = (500 + 1000)/2
x = (750 + 1000)/2
x = 875


2. What was the original size of the colony if the colony disappeared by the end of the 6th day?

suppose the no of bactaria at the begaining = x
the no of bactaria next morning = 2x
2{2(2[2 {2 (2x - 1000) - 1000} - 1000] - 1000) - 1000} - 1000 = 0
solving for x, x = 984.375



why is it 2x?

my initial pass at the reading was x^2..

can someone explain to me?
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Re: bacteria - algebra [#permalink] New post 20 Dec 2007, 10:08
mjoeb wrote:
GMAT TIGER wrote:
GMAT TIGER wrote:
bmwhype2 wrote:
A colony of bacteria doubles every morning while every evening 1000 bacteria die.

What was the original size of the colony if the colony disappeared by the end of the 3rd day?




why is it 2x?

my initial pass at the reading was x^2..

can someone explain to me?


Doubles = 2 times (Double of 10 = 20, double of that is 40, etc.)
Squared = x^2
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Re: bacteria - algebra [#permalink] New post 20 Dec 2007, 10:34
GK_Gmat wrote:
mjoeb wrote:
GMAT TIGER wrote:
GMAT TIGER wrote:
bmwhype2 wrote:
A colony of bacteria doubles every morning while every evening 1000 bacteria die.

What was the original size of the colony if the colony disappeared by the end of the 3rd day?




why is it 2x?

my initial pass at the reading was x^2..

can someone explain to me?


Doubles = 2 times (Double of 10 = 20, double of that is 40, etc.)
Squared = x^2



why is this one

3*2^(n-1)?
Population of a bacteria colony doubles every day. If it was started 6 days ago when 3 bacteria were born in a deserted colony and each bacteria lives for 12 days, how large is the colony today?
Re: bacteria - algebra   [#permalink] 20 Dec 2007, 10:34
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