johnstonj59
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Please Help:
According to Newton's Law of Cooling, if a body with temperature [tex]T_{1}[/tex] is placed in surroundings with temperature [tex]T_{0}[/tex], different from that of [tex]T_{1}[/tex], the body will either cool or warm to temperature [tex]T_{T}[/tex] after t minutes, where:
[tex]T(t)=T_{0} +(T_{1}-T_{0})e^k^t[/tex]
and [tex]K[/tex] 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.

Respuesta :

PunIntended

Answer:

41 degrees F

Step-by-step explanation:

(Ah, calculus...)

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

[tex]T(15)=0+(140-0)e^{-0.0815*15} =41.229[/tex]

41.229 ≈ 41

So, the answer is 41 degrees F.

Hope this helps!

amna04352

Answer:

41°F

Step-by-step explanation:

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

T(15) = 140e^(-0.0815×15)

T(15) = 41.22902187