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# The restorative power of sleep is graphically approximated by the func

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Math Expert
Joined: 02 Sep 2009
Posts: 52906
The restorative power of sleep is graphically approximated by the func  [#permalink]

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30 Nov 2016, 02:04
00:00

Difficulty:

65% (hard)

Question Stats:

61% (01:52) correct 39% (02:00) wrong based on 250 sessions

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The restorative power of sleep is graphically approximated by the function −x^2 + 16x + 36, where the x-axis measures sleeping hours and the y-axis measures the restoration value. After how many hours does sleep no longer perform restorative duties according to the function?

A. −2
B. 4
C. 8
D. 13
E. 18

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Re: The restorative power of sleep is graphically approximated by the func  [#permalink]

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30 Nov 2016, 03:50
1
Bunuel wrote:
The restorative power of sleep is graphically approximated by the function −x^2 + 16x + 36, where the x-axis measures sleeping hours and the y-axis measures the restoration value. After how many hours does sleep no longer perform restorative duties according to the function?

A. −2
B. 4
C. 8
D. 13
E. 18

The restorative power is given by $$-x^2 + 16x + 36$$.

We want the value of x (number of hours) for which it will become 0.

-x^2 + 16x + 36 = 0
x = 18, -2

After 18 hours, the graph will be negative so there will be no positive restoration value.
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Re: The restorative power of sleep is graphically approximated by the func  [#permalink]

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30 Nov 2016, 06:19
The restorative power is given by the equation -x^{2}+16x+36, which is equal to x^2-16x-36. We are told that the restoration value is in the y-axis, and we want to find out after how much sleep we would not get any restoration for our sleep.
So if y becomes 0, we have x^2-16x-36=0.
or
(x-18)(x+2)=0
Which means that x=18 or x=-2
Since we are counting hours of sleep, the answer cannot be negative, thus x=18 and the answer is E.
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Re: The restorative power of sleep is graphically approximated by the func  [#permalink]

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16 Jun 2017, 22:50
1
Bunuel wrote:
The restorative power of sleep is graphically approximated by the function −x^2 + 16x + 36, where the x-axis measures sleeping hours and the y-axis measures the restoration value. After how many hours does sleep no longer perform restorative duties according to the function?

A. −2
B. 4
C. 8
D. 13
E. 18

This question is simple yet has a very subtle trap answer- in order to find the values of x we must factor the equation- if you simply plug in values and solve for 0 you would also find that -2 and 18 equal 0. However, theoretically, you cannot have a negative amount of sleep therefore the answer is simply 18. This is just a matter of reading the question

Thus
"E"
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Re: The restorative power of sleep is graphically approximated by the func  [#permalink]

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15 Oct 2018, 06:41
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Re: The restorative power of sleep is graphically approximated by the func   [#permalink] 15 Oct 2018, 06:41
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