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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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02 Jul 2017, 12:00
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64% (01:24) correct 36% (01:34) wrong based on 241 sessions

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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 * $$10 ^ 6$$
[Reveal] Spoiler: OA

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

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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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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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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)

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

[Reveal] Spoiler:
B

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

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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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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.

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

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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
Re: Four hours from now, the population of a colony of bacteria will reach   [#permalink] 15 Jan 2018, 03:33
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# Four hours from now, the population of a colony of bacteria will reach

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