Question

You open a case of Cherry Coke from the garage to put cans in the refrigerator. You put the

85°F cans in the 36°F refrigerator. After 5 minutes, the can temperature has gone down to
71°F. Find the constant "k" using Newton's Law of Cooling.

Answer 1

9514 1404 393

Answer:

k ≈ -0.06729

Explanation:

The initial temperature difference is 85 -36 = 49 degrees. After 5 minutes, the temperature difference is 71 -36 = 35 degrees. The constant k is the natural log of the ratio of these temperature differences, divided by the time unit.

k = ln(35/49)/5 ≈ -0.06729

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The equation for the temperature T of the can in the refrigerator is ...

T = 49e^(-0.06729t) +36

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Additional comment

Be careful with the sign. If you're filling in k in e^(-kt), then the sign of k will be positive. Above, we have taken the form of the exponential term to be e^(kt), so k is negative.