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 kt and k is a constant. 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. The temperature is about a0degrees Fahrenheit.

Question

Mathematics

Irwin

18 February, 18:40

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 kt and k is a constant. 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. The temperature is about a0degrees Fahrenheit.

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Alfred Gilmore · Answer 1

We can substitute the given values into the equation for T, given the surrounding temperature T0 = 0, initial temperature T1 = 140, constant k = - 0.0815, and time t = 15 minutes.

T = 0 + (140 - 0) e^ (-0.0815*15) = 140e^ (-1.2225) = 41.23 °F