Question

Newton's Law of Cooling The temperature of a cup of coffee t min after it is poured is given by the following equation where T is measured in degrees Fahrenheit. T = 80 + 95e−0.048t(a) What was the temperature (in degrees Fahrenheit) of the coffee when it was poured? °F(b) When (in minutes) will the coffee be cool enough to drink (say, 120°F)? (Round your answer to one decimal place.) min

Answer 1

The temperature of the coffee when it was poured is 175°F. It will take approximately 17.67 minutes for the coffee to cool enough to drink at 120°F.

Step-by-step explanation:

(a) The temperature of the coffee when it was poured can be found by substituting t = 0 into the equation. T = 80 + 95e-0.048(0) = 80 + 95e0 = 80 + 95(1) = 175°F.

(b) To find when the coffee will be cool enough to drink, we need to solve the equation 120 = 80 + 95e-0.048t for t. Subtracting 80 from both sides gives 40 = 95e-0.048t. Dividing both sides by 95 gives 0.421 = e-0.048t. Taking the natural logarithm of both sides gives -0.848 ≈ -0.048t. Dividing both sides by -0.048 gives t ≈ 17.67 minutes.

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