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# The temperature of a certain cup of coffee 10 minutes after

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Intern
Joined: 16 Apr 2010
Posts: 19
The temperature of a certain cup of coffee 10 minutes after  [#permalink]

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28 Jul 2010, 08:11
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Difficulty:

25% (medium)

Question Stats:

77% (02:37) correct 23% (02:43) wrong based on 526 sessions

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

A. 65
B. 75
C. 80
D. 85
E. 90
Math Expert
Joined: 02 Sep 2009
Posts: 50661
Re: The temperature of a certain cup of coffee 10 minutes after  [#permalink]

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29 Jul 2010, 03:03
7
4
kilukilam wrote:
The tempreature of a certain cup of coffee 10 minutes after it was poured was 120 degree Faranite. If the temp F of the coffee t minues after it was poured can be determinde by the formula F=120 (2^-at)+60 , where F is degree Fahrenhite and a is constant, then the tempreature of the cofffee 30 minues after it was poured was how many degree fahrenhite

a. 65
b. 75
c. 80
d. 85
e. 90

We have the formula for calculating temperature: $$F=120*2^{-at}+60$$ and the value for $$t=10$$ --> $$F(t=10)=120=120*2^{-10a}+60$$ --> $$\frac{1}{2^{10a}}=\frac{1}{2}$$ --> $$10a=1$$ --> $$a=0.1$$. So formula is $$F=120*2^{-0.1t}+60$$

Now for $$t=30$$ the temperature in Fahrenheits will be $$F=120*2^{-0.1*30}+60=\frac{120}{2^3}+60=75$$.

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Location: Germany
GMAT 1: 660 Q45 V36
GPA: 3.51
Re: The temperature of a certain cup of coffee 10 minutes after  [#permalink]

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12 Mar 2014, 04:11
9
4
First, we have to find a.

We know that after t=10 minutes the temperature F=120 degrees.

Hence:
120 = 120*(2^-10a)+60
60 = 120*(2^-10a)
60/120 = 2^-10a
1/2 = 2^-10a
2^-1 = 2^-10a
-1 = -10a
1/10 = a

Now we need to find F after t=30 minutes:
F = 120*(2^-1/10*30)+60
F = 120* (2^-3) +60
F = 120* (1/2^3) +60
F = 120*1/8 +60
F = 15+60 = 75

##### General Discussion
Manager
Joined: 16 Apr 2010
Posts: 200
Re: The temperature of a certain cup of coffee 10 minutes after  [#permalink]

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28 Jul 2010, 10:57
Hi,

Since F=120 (2^-at)+60,
replace F=120, t=10 to find a.
Once you find a, then to find the temperature 30 min after it was poured simply replace
t=30 and value of a in the equation.

regards,
Jack
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Concentration: Strategy, General Management
GMAT 1: 680 Q48 V34
Re: The temperature of a certain cup of coffee 10 minutes after  [#permalink]

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28 Jul 2010, 12:26
1
Is the question correctly written?? I am unable to find the solution.

$$F= 120* (\frac{1}{2^at}) + 60$$
Is this formula correct?
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Intern
Joined: 04 Jul 2013
Posts: 26
Schools: ISB '16
Re: The temperature of a certain cup of coffee 10 minutes after  [#permalink]

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17 Apr 2014, 00:36
Substitute the values f=120 and t=10 in given equation, this gives value of a=0.1

now equation is f=120(2^-0.1t)+60

substitute t=30 in above equation to find f

Intern
Joined: 06 Mar 2015
Posts: 7
Re: The temperature of a certain cup of coffee 10 minutes after  [#permalink]

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27 Mar 2015, 05:34
1
Can someone explain me how
1/2 = 2^-10a becomes

2^-1 = 2^-10a
Intern
Joined: 17 Feb 2015
Posts: 27
GPA: 3
Re: The temperature of a certain cup of coffee 10 minutes after  [#permalink]

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27 Mar 2015, 05:59
1
lzielen wrote:
Can someone explain me how
1/2 = 2^-10a becomes

2^-1 = 2^-10a

Hi lzielen!

$$\frac{1}{2}$$ is $$2^{-1}$$.

$$x^{-n} = 1/x^n$$
Manager
Joined: 05 Dec 2016
Posts: 115
Re: The temperature of a certain cup of coffee 10 minutes after  [#permalink]

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22 Mar 2018, 08:27
Hussain15 wrote:
Is the question correctly written?? I am unable to find the solution.

$$F= 120* (\frac{1}{2^at}) + 60$$
Is this formula correct?

a*t is the power of 2 it is 2^(-at)
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Intern
Joined: 13 Sep 2018
Posts: 1
Re: The temperature of a certain cup of coffee 10 minutes after  [#permalink]

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13 Sep 2018, 04:47
Bunuel wrote:
kilukilam wrote:
The tempreature of a certain cup of coffee 10 minutes after it was poured was 120 degree Faranite. If the temp F of the coffee t minues after it was poured can be determinde by the formula F=120 (2^-at)+60 , where F is degree Fahrenhite and a is constant, then the tempreature of the cofffee 30 minues after it was poured was how many degree fahrenhite

a. 65
b. 75
c. 80
d. 85
e. 90

We have the formula for calculating temperature: $$F=120*2^{-at}+60$$ and the value for $$t=10$$ --> $$F(t=10)=120=120*2^{-10a}+60$$ --> $$\frac{1}{2^{10a}}=\frac{1}{2}$$ --> $$10a=1$$ --> $$a=0.1$$. So formula is $$F=120*2^{-0.1t}+60$$

Now for $$t=30$$ the temperature in Fahrenheits will be $$F=120*2^{-0.1*30}+60=\frac{120}{2^3}+60=75$$.

You're solution is quite clear to me, I only have one question:

How do you conduct this step: $$\frac{1}{2^{10a}}=\frac{1}{2}$$ --> $$10a=1$$

I would solve it like this:

$$\frac{1}{2^{10a}}=\frac{1}{2}$$ --> 2^-1 = 2^-10a --> -1 lg(2) = -10a lg(2) --> 1 = 10a

Is there a easier possibility? Is it even right to solve the question by the use of logarithm?

Math Expert
Joined: 02 Sep 2009
Posts: 50661
Re: The temperature of a certain cup of coffee 10 minutes after  [#permalink]

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13 Sep 2018, 04:50
DominikSterk wrote:
Bunuel wrote:
kilukilam wrote:
The tempreature of a certain cup of coffee 10 minutes after it was poured was 120 degree Faranite. If the temp F of the coffee t minues after it was poured can be determinde by the formula F=120 (2^-at)+60 , where F is degree Fahrenhite and a is constant, then the tempreature of the cofffee 30 minues after it was poured was how many degree fahrenhite

a. 65
b. 75
c. 80
d. 85
e. 90

We have the formula for calculating temperature: $$F=120*2^{-at}+60$$ and the value for $$t=10$$ --> $$F(t=10)=120=120*2^{-10a}+60$$ --> $$\frac{1}{2^{10a}}=\frac{1}{2}$$ --> $$10a=1$$ --> $$a=0.1$$. So formula is $$F=120*2^{-0.1t}+60$$

Now for $$t=30$$ the temperature in Fahrenheits will be $$F=120*2^{-0.1*30}+60=\frac{120}{2^3}+60=75$$.

You're solution is quite clear to me, I only have one question:

How do you conduct this step: $$\frac{1}{2^{10a}}=\frac{1}{2}$$ --> $$10a=1$$

I would solve it like this:

$$\frac{1}{2^{10a}}=\frac{1}{2}$$ --> 2^-1 = 2^-10a --> -1 lg(2) = -10a lg(2) --> 1 = 10a

Is there a easier possibility? Is it even right to solve the question by the use of logarithm?

$$\frac{1}{2^{10a}}=\frac{1}{2}$$;

Cross-multiply: $$2=2^{10a}$$

Equate the powers: $$10a=1$$
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Re: The temperature of a certain cup of coffee 10 minutes after &nbs [#permalink] 13 Sep 2018, 04:50
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