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formula question

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formula question

by smallsorrow » Tue Nov 18, 2008 12:58 am
The temperature of a certain cup of coffee is 120 Fahrenheit 10 minutes after it was poured in a cup. If the temperature F of the coffee t minutes later is defined 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 later is how many degrees fahrenheit?
65, 75, 80, 85 or 90 ?

Anyone know how to solve this quickly? Took me over three minutes...
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Re: formula question

by logitech » Tue Nov 18, 2008 1:11 am
smallsorrow wrote:The temperature of a certain cup of coffee is 120 Fahrenheit 10 minutes after it was poured in a cup. If the temperature F of the coffee t minutes later is defined 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 later is how many degrees fahrenheit?
65, 75, 80, 85 or 90 ?

Anyone know how to solve this quickly? Took me over three minutes...
120 = 120(@@)+60

@@ = 1/2 = 2^-1 = 2^-10a s0m a=1/10

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

= 120/8 + 60

= 75

Explaining takes time but solving should be between 1-2 minutes. Or even less than a minute, if you are fast.
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Re: formula question

by rohangupta83 » Tue Nov 18, 2008 2:35 am
logitech wrote:
120 = 120(@@)+60

@@ = 1/2 = 2^-1 = 2^-10a s0m a=1/10

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

= 120/8 + 60

= 75

Explaining takes time but solving should be between 1-2 minutes. Or even less than a minute, if you are fast.
This is likely the only way to do this problem.

1st solve for A with F = 120 and t = 10
2nd solve for F with 'A' from the 1st equation and t = 30

Answer 75
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