The restorative power of sleep is graphically approximated b

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Wed Feb 27, 2019 8:25 pm

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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

OA E

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Feb 28, 2019 3:25 am

BTGmoderatorDC 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

Multiplying the equation by -1, we get:
y = x² - 16x - 36
y = (x-18)(x+2)

The restorative power -- the value of y -- is equal to 0 when x=18 or x=-2.
Since the time cannot be a negative value, only x = 18 hours is viable.

The correct answer is E.

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swerve: Legendary Member; Posts: 2604; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Fri Mar 01, 2019 9:25 am

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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by Scott@TargetTestPrep » Mon Mar 04, 2019 7:05 pm

BTGmoderatorDC 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

OA E

Source: Veritas Prep

Sleep no longer performs any restorative duties if the value of the function is below 0. So let’s set the function equal to 0 and solve for x:

-x^2 + 16x + 36 = 0

x^2 - 16x - 36 = 0

(x - 18)(x + 2) = 0

x = 18 or x = -2

We see that sleep performs a restorative duty when x is between -2 and 18 (just substitute any value between -2 and 18 into the function, and the function value will be positive). Therefore, sleep will not perform a restorative duty after 18 hours (that is, substitute any value greater than 18 into the function, and the function value will be negative).

Answer: E

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