# Need help with simple cooling problem.

I just need someone to confirm my answer so I can be certain that my book has a typo and I am not making a some minuscule mistake that is leading me to the wrong answer.

A piece of metal is heated to 300 degrees Celsius and then placed in a cooling liquid at 50 degrees Celsius. After 4 minutes, the metal has cooled to 175 degrees Celsius. Find it's temperature after 12 minutes.

Equation: F(t)= To+ Ce^-kt

e= Euler's number

I started out solving for k

175= 50 + 300e^-k4
-50 -50

125=300e^-k4
/300 /300
-The Celsius units cancel out-

125/300=e^-k4
Ln Ln

Ln(125/300)= -4k
/-4 /-4

k= .21887

then I plug in the value of k and solve for what temperature the metal will be after 12 minutes have passed.

F(t)= 50+300e^-.21887*12

= 71.700

I end up getting the answer above but the book says the answer is 81.25

haruspex
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I just need someone to confirm my answer so I can be certain that my book has a typo and I am not making a some minuscule mistake that is leading me to the wrong answer.

A piece of metal is heated to 300 degrees Celsius and then placed in a cooling liquid at 50 degrees Celsius. After 4 minutes, the metal has cooled to 175 degrees Celsius. Find it's temperature after 12 minutes.

Equation: F(t)= To+ Ce^-kt

e= Euler's number

I started out solving for k

175= 50 + 300e^-k4
-50 -50

125=300e^-k4
/300 /300
-The Celsius units cancel out-

125/300=e^-k4
Ln Ln

Ln(125/300)= -4k
/-4 /-4

k= .21887

then I plug in the value of k and solve for what temperature the metal will be after 12 minutes have passed.

F(t)= 50+300e^-.21887*12

= 71.700

I end up getting the answer above but the book says the answer is 81.25

If you plug t=0 into your first equation, does it give the right initial temperature?

xsgx
If you plug t=0 into your first equation, does it give the right initial temperature?
Wow.. I can't believe I missed that. Thank you.

haruspex