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When an object is removed from a furnace and placed in an environment with a constant temperature of 70°F, its core temperature is 1030°F. Seven hours later the core temperature is 330°F. Explain why there must exist a time in the interval, (0, 7), when the temperature is decreasing at a rate of 100°F per hour.

Respuesta :

IthaloAbreu

Answer:

We can prove it using the mean value theorem, as explained below.

Explanation:

Let's call f(t) the temperature of the core at the time t. So, in beginning, t= 0, f(0) = 1030ºF, and after 7 hours, f(7) = 330ºF.

The rate of decreasing can be calculated applying the MVT (Mean Value Theorem), and it would be the temeperature at 7 hours minus the temperature at t = 0 divided by 7 (which is the time interval), so:

r = (330 - 1030)/7

r = -700/7

r = -100ºF per hour

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