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Four hours from now, the population of a colony of bacteria will reach

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Four hours from now, the population of a colony of bacteria will reach  [#permalink]

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New post 02 Jul 2017, 12:00
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Four hours from now, the population of a colony of bacteria will reach 1.28 * \(10 ^ 6\). If the population of the colony doubles every 4 hours, what was the population 12 hours ago?

A. 6.4 * \(10 ^ 2\)
B. 8.0 * \(10 ^ 4\)
C. 1.6 * \(10 ^ 5\)
D. 3.2 * \(10 ^ 5\)
E. 8.0 * \(10 ^ 6\)

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Re: Four hours from now, the population of a colony of bacteria will reach  [#permalink]

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New post 02 Jul 2017, 12:16
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Population after 4 hours is given, take it as x

So current population is x/2

Before 12 hours is x/16

Option B




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Re: Four hours from now, the population of a colony of bacteria will reach  [#permalink]

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New post 02 Jul 2017, 12:18
These kind of questions, are best done when we go backwards.

1280000 when halved gives 640000(4 hours ago)
4 more hours ago the population of the colony of bacterial colony would be 320000
4 more hours ago, the population will be 160000
4 more hours ago, the population will be 80000 which is 8 * \(10 ^ 4\)(Option B)
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Re: Four hours from now, the population of a colony of bacteria will reach  [#permalink]

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New post 02 Jul 2017, 14:48
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carcass wrote:
Four hours from now, the population of a colony of bacteria will reach 1.28 * \(10 ^ 6\). If the population of the colony doubles every 4 hours, what was the population 12 hours ago?

6.4 * \(10 ^ 2\)
8.0 * \(10 ^ 4\)
1.6 * \(10 ^ 5\)
3.2 * \(10 ^ 5\)
8.0 * \(10 ^ 6\)


Let's work backwards.

Population 4 hours in future: 1.28 x 10^6
Population now: 0.64 x 10^6 (half the population 4 hours in future)
Population 4 hours ago: 0.32 x 10^6 (half the current population)
Population 8 hours ago: 0.16 x 10^6 (half the population 4 hours ago)
Population 12 hours ago: 0.08 x 10^6 (half the population 8 hours ago)

Now check the answer choices.
Only answer choices B and E have the same format with 8 times some power of 10
Answer choice E definitely doesn't match, so the correct answer must be B

For any doubters out there, notice that:
0.08 x 10^6 = (8.0) x (10^-2) x 10^6
= 8.0 x 10^4

Answer:

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Re: Four hours from now, the population of a colony of bacteria will reach  [#permalink]

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New post 16 Oct 2017, 18:23
It is possible to do using powers to simplify:
(future) 1.28 x 10^6
Going back 4 times from +4y to -12y: multiply by 1/(2^4)
1.28 x 10^6 = 128 x 10^4 = 2^7 x 10^4 == you could stop here looking to the possible answers
(2^7 x 10^4) / 2^4 = 2^3 x 10^4 = 8 x 10^4
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Re: Four hours from now, the population of a colony of bacteria will reach  [#permalink]

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New post 19 Oct 2017, 10:26
carcass wrote:
Four hours from now, the population of a colony of bacteria will reach 1.28 * \(10 ^ 6\). If the population of the colony doubles every 4 hours, what was the population 12 hours ago?

A. 6.4 * \(10 ^ 2\)
B. 8.0 * \(10 ^ 4\)
C. 1.6 * \(10 ^ 5\)
D. 3.2 * \(10 ^ 5\)
E. 8.0 * \(10 ^ 6\)



Since the population doubles every 4 hours and the population will be 1.28 x 10^6 four hours from now, the current population must be half of 1.28 x 10^6, or ½(1.28 x 10^6) = 0.64 x 10^6.

Thus:

4 hours ago, the population was half the current population: ½(0.64 x 10^6) = 0.32 x 10^6.

8 hours ago, the population was half the population 4 hours ago: ½(0.32 x 10^6) = 0.16 x 10^6.

Finally, 12 hours ago the population was half the population 8 hours ago: ½(0.16 x 10^6) = 0.08 x 10^6 = 8 x 10^-2 x 10^6 = 8 x 10^4.

Answer: B
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Re: Four hours from now, the population of a colony of bacteria will reach  [#permalink]

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New post 15 Jan 2018, 03:33
It will double every 4 hour => if 4 hours from now the population is 1.28 * 10^6
=> now the population is 1.28 * 10^6 / 2

It will double (x2) every 4 hour => 12 hours ago, the population is 1/ 2^ 3 = 1/8 the population now (3 = 12/4)
=> The population 12 hours ago = 1.28 * 10^6 /2 * 1/8 = 8 * 10^4

=> B
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Four hours from now, the population of a colony of bacteria will reach  [#permalink]

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New post 06 May 2018, 06:19
carcass wrote:
Four hours from now, the population of a colony of bacteria will reach 1.28 * \(10 ^ 6\). If the population of the colony doubles every 4 hours, what was the population 12 hours ago?

A. 6.4 * \(10 ^ 2\)
B. 8.0 * \(10 ^ 4\)
C. 1.6 * \(10 ^ 5\)
D. 3.2 * \(10 ^ 5\)
E. 8.0 * \(10 ^ 6\)



pushpitkc, is my approach / reasoning correct ? :)

1.28 * \(10 ^ 6\) means we need to move decimal point 6 points to the right so it is 1,280,000, so i just leave out zeros and work with 128

if in 4 hours the population will be 128, then now it is 64

4 hours ago it was 32
8 hours ago 16
12 hrs ago 8

so all i need is to add 4 zeros and express it like this \(8*10^4\) :)

one thing I didn't get why in answer option B. 8.0 * \(10 ^ 4\) \(8\) is expressed as \(8.0\) and not just \(8\) I mean with one zero after decimal point... :?
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Four hours from now, the population of a colony of bacteria will reach  [#permalink]

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New post 06 May 2018, 08:13
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dave13 wrote:
carcass wrote:
Four hours from now, the population of a colony of bacteria will reach 1.28 * \(10 ^ 6\). If the population of the colony doubles every 4 hours, what was the population 12 hours ago?

A. 6.4 * \(10 ^ 2\)
B. 8.0 * \(10 ^ 4\)
C. 1.6 * \(10 ^ 5\)
D. 3.2 * \(10 ^ 5\)
E. 8.0 * \(10 ^ 6\)



pushpitkc, is my approach / reasoning correct ? :)

1.28 * \(10 ^ 6\) means we need to move decimal point 6 points to the right so it is 1,280,000, so i just leave out zeros and work with 128

if in 4 hours the population will be 128, then now it is 64

4 hours ago it was 32
8 hours ago 16
12 hrs ago 8

so all i need is to add 4 zeros and express it like this \(8*10^4\) :)

one thing I didn't get why in answer option B. 8.0 * \(10 ^ 4\) \(8\) is expressed as \(8.0\) and not just \(8\) I mean with one zero after decimal point... :?


Hi dave13

This problem is best solved when we go backwards!

8 *10^4 = 80000
Now see the sequence when we double the population of the colony of bacteria
80000 * 2 = 160000 | 160000 * 2 = 320000 | 320000 * 2 = 640000 | 640000 * 2 = 1280000
(You can see that 12 hours from the start, the population has increased
from 8 *10^4 to 6.4 *10^5 and then to 1.28 * 10^6)

Your approach is perfect otherwise. All you need to understand is this part of why the ZEROES increase!

Hope this helps you!
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Re: Four hours from now, the population of a colony of bacteria will reach  [#permalink]

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New post 06 May 2018, 14:13
1.28E6 = 128E4. 12 hours before now = 2^4 --> 128E4 / 2^4 = 128E4 / 16 = 128/16 = 8E4.
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Re: Four hours from now, the population of a colony of bacteria will reach &nbs [#permalink] 06 May 2018, 14:13
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