Question

You place a cup of 220 degree F hot chocolate on a table in a room that is 72 degrees F, and 12 minutes later, it is 205 degrees F. Approximately how long will it be before the coffee is 175 degrees F? Round to the nearest minute. Use Newtons law of cooling: T(t)=Ta+(To-Ta)e^-kt
Please help I don't understand!

Answer 1

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what do u think it is?

Answer 2

So i think i plug in t(175)=220(72-220)e^k*175 im not sure

Answer 3

T0 is the initial temp of the coffee .... 220 degrees
Ta is the temp of the room ....... 72 degrees

To find out when the temp is 175, you must solve for the "k" value.
Given that T(12) = 205.

\[205 = 72 + (220-72) e^{-12k}\]
\[k = \frac{\ln (\frac{205-72}{220-72})}{-12}\]
subbing k back into the cooling equation...
\[T(t) = 72 + (220-72)(\frac{205-72}{220-72})^{t/12}\]
Now plug in 175 for T(t) and solve for "t", the time it takes to cool the coffee to 175 degrees
\[\large t = 12\left(\begin{matrix}\frac{\ln(\frac{175-72}{220-72})}{\ln(\frac{205-72}{220-72})} \\ \end{matrix}\right)\]

Answer 4

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