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According to Newton's Law of Cooling, if a body with temperature
T_(1) is placed in surroundings with temperature
T_(0), different from that of
T_(1), the body will either cool or warm to temperature
T_(T) after t minutes, where:

T(t)=T_(0) +(T_(1)-T_(0))e^k^t
and
K is a constant.

If a cup of coffee with temperature 140°F is placed in a freezer with temperature 0°F. The constant k ≅ -0.0815. Use Newton's Law of Cooling to find the coffee's temperature, to the nearest degree Fahrenheit, after 15 minutes.

User Stgatilov
by
6.2k points

2 Answers

5 votes

Answer:

41°F

Explanation:

T(t) = 0 + (140 - 0)e^(-0.0815t)

T(15) = 140e^(-0.0815×15)

T(15) = 41.22902187

User Sergii Rudenko
by
6.6k points
0 votes

Answer:

41 degrees F

Explanation:

(Ah, calculus...)

In this case,
T_0 is 0 degrees F and
T_1 is 140 degrees F. k = -0.0815 and t = 15. Plug all these values into the equation:


T(15)=0+(140-0)e^(-0.0815*15) =41.229

41.229 ≈ 41

So, the answer is 41 degrees F.

Hope this helps!

User Kausha Mehta
by
6.2k points
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