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3 years ago

MATH PEOPPE PLEASE HELP

Mathematics

1 answer:

muminat3 years ago

6 0

Answer:

156 °F

Step-by-step explanation:

Newton's Law of Heating results in the exponential function you show in your problem statement. We can use the given starting and "in-progress" temperatures and times to solve for the value of the factor "k" in the exponential function.

$T(t)=T_\infty+(T_0-T_\infty)e^{-kt}\\\\T(2.5)=123=305+(72-305)e^{-k\cdot2.5}\qquad\text{substitute given temps and times}\\\\\dfrac{123-305}{72-305}=e^{-2.5k}=\dfrac{182}{233}\qquad\text{subtract 305, divide by $(72-305)$}\\\\k=\dfrac{-1}{2.5}\ln\dfrac{182}{233}\approx0.0988127\approx0.099\qquad\text{rounded to 3 places}$

Then the temperature after 4.5 hours is ...

T(4.5) = 305 -233e^(-0.099·4.5) ≈ 156 . . . . °F

_____

<em>Additional comment</em>

It will take about 6.3 hours for the turkey temperature to reach 180 °F.

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