Use Newton's law of Cooling. Can I get some help please? THANKS!

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1 Answer
Noah G
Jan 15, 2018

#35˚F#.

Explanation:

Start by identifying the parameters.

We know #T_0# will be the initial temperature of the coffee, #102˚F#. #C# will be the temperature of the surrounding environment, or #0˚F#. #T# is the temperature after being in the freezer for #8# minutes, which is our #t# value. Essentially we will be solving for #k# in order to solve for the temperature after #13# minutes.

#52.5 = 0 + (102 - 0)e^(8k)#

#52.5 = 102e^(8k)#

#0.5147 = e^(8k)#

#ln(0.5147) = ln(e^(8k))#

#ln(0.5147) = 8k#

#k = -0.083#

Now we're going to solve for #T# with #t = 13# minutes.

#T = 0 + (102 - 0)e^(13(-0.083))#

#T = 34.67˚F#

To the nearest degree, #35˚F#.

Hopefully this helps!

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