Question from mba.com mock test

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Cybermusings: Legendary Member; Posts: 559; Joined: Tue Mar 27, 2007 1:29 amFollowed by: 2 members; Thanked: 5 times

by Cybermusings » Sat Apr 14, 2007 1:26 am

The temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees Farenheit. If the temperature F of the coffee t minutes after it was poured can be determined by F = 120(2^-at)+60, where F is in Farenheit, and "a" is a constant, then the temperature of the coffee 30 minutes after it was poured was how many degrees?

1) 65
2) 75
3) 80
4) 85
5) 90

Please answer with detailed explanation. I am not getting this one right..

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Source: Beat The GMAT — Problem Solving | Sat Apr 14, 2007 1:26 am

ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

Re: Question from mba.com mock test

by ajith » Sat Apr 14, 2007 3:03 am

Cybermusings wrote:The temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees Farenheit. If the temperature F of the coffee t minutes after it was poured can be determined by F = 120(2^-at)+60, where F is in Farenheit, and "a" is a constant, then the temperature of the coffee 30 minutes after it was poured was how many degrees?

1) 65
2) 75
3) 80
4) 85
5) 90

Please answer with detailed explanation. I am not getting this one right..

the temperature F of the coffee t minutes after it was poured can be determined by F = 120(2^-at)+60

Given that F aftter 10 mins =120
=> 120 = 120 (2^-10a) +60
2 = 2 (2^-10a ) +1
1= 2(2^-10a )
2^(1-10a)=2^0
=> 1-10a =0
=> a=1/10
Temp after 30 mins = 120 (2^-1/10*30)+60
= 120 (1/8) +60
= 75
Hope it is clear!

Always borrow money from a pessimist, he doesn't expect to be paid back.

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Cybermusings: Legendary Member; Posts: 559; Joined: Tue Mar 27, 2007 1:29 amFollowed by: 2 members; Thanked: 5 times

by Cybermusings » Sat Apr 14, 2007 11:06 am

Hey thanks dude!

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GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8153; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Mon May 20, 2019 6:07 pm

Cybermusings wrote:The temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees Farenheit. If the temperature F of the coffee t minutes after it was poured can be determined by F = 120(2^-at)+60, where F is in Farenheit, and "a" is a constant, then the temperature of the coffee 30 minutes after it was poured was how many degrees?

1) 65
2) 75
3) 80
4) 85
5) 90

First we need to find the value of a using F = 120 and t = 10:

120 = 120 * 2^(-10a) + 60

60 = 120 * 2^(-10a)

1/2 = 2^(-10a)

2^(-1) = 2^(-10a)

With a common base, we can equate the exponents:

-1 = -10a

a = 1/10

Now we can find F using a = 1/10 and t = 30:

F = 120 * 2^(-(1/10)(30)) + 60

F = 120 * 2^(-3) + 60

F = 120 * 1/8 + 60

F = 15 + 60

F = 75

Answer: 2/B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Tue May 21, 2019 6:32 am

Cybermusings wrote:The temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees Farenheit. If the temperature F of the coffee t minutes after it was poured can be determined by F = 120(2^-at)+60, where F is in Farenheit, and "a" is a constant, then the temperature of the coffee 30 minutes after it was poured was how many degrees?

1) 65
2) 75
3) 80
4) 85
5) 90

The temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees Fahrenheit.

So, 120 = 120 * 2^[(-a)(10)] + 60
Divide both sides by 60: 2 = 2 * 2^[(-a)(10)] + 1
1 = 2 * 2^[(-a)(10)]
1/2 = 2^[(-a)(10)]
Since 2^(-1) = 1/2, we know that (-a)(10) = -1
So, a = 1/10

So, the formula is f = 120 * 2^[(-1/10)(t)] + 60

The temperature of the coffee 30 minutes after it was poured was how many degrees Fahrenheit?
f = 120 * 2^[(-1/10)(30)] + 60
= 120 * 2^[-3] + 60
= 120 * (1/8) + 60
= 15 + 60
= 75

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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