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Math Q2 -
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prashanth.guru
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The temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees Fahrenheit.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
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
= B
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The given formula is F = 120*2^(-at) + 60.The temperature of a certain cup of coffee 10 minutes it was poured was 120 degree Fahrenheit. If 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 degree Fahrenheit?
A. 65
B. 75
C. 80
D. 85
E. 90
Ignore 2^(-at).
We need to determine the MULTIPLIER: the factor by which 120 must be multiplied for every 10 minutes.
Let x = the multiplier.
The formula becomes F = 120x + 60.
Since after 10 minutes, F=120:
120 = 120x + 60
x = 1/2.
Thus, for every 10 minutes, 120 must be multiplied by 1/2.
Thus, to determine the value of F after 30 minutes, 120 must be multiplied by 1/2 three times:
F = 120(1/2)³ + 60
F = 75.
The correct answer is B.
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