Setting up and solving 2 nonlinear equations (Newton's Law of Cooling)

Original question:

http://i57.photobucket.com/albums/g2...at100030PM.png

The instructor gave explicit step-by-step instructions on what she wanted.

Step 1:

http://i57.photobucket.com/albums/g2...at100558PM.png

My [correct] solution to step 1:

http://i57.photobucket.com/albums/g2...001_220957.jpg

Step 2:

http://i57.photobucket.com/albums/g2...at101438PM.png

My [correct] solution to step 2:

http://i57.photobucket.com/albums/g2...001_221035.jpg

Step 3:

http://i57.photobucket.com/albums/g2...at101638PM.png

My [correct] solution to step 3:

http://i57.photobucket.com/albums/g2...001_221059.jpg

Step 4 (this is where the problems begin):

http://i57.photobucket.com/albums/g2...at101843PM.png

My solution to step 4 (now, this is a valid method to solve the problem BUT is NOT how she wants it to be solved!):

http://i57.photobucket.com/albums/g2...001_221107.jpg

Step 5

http://i57.photobucket.com/albums/g2...at102131PM.png

My solution to step 5 (again, I get the CORRECT answer; but my process, according to my instructor is incorrect based on the given instructions):

http://i57.photobucket.com/albums/g2...001_221113.jpg

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**If someone can please assist me in coming up with two nonlinear equations in the 2 variable t1 and K (step 4), I would forever appreciate you!**

Thank you very much.

Re: Setting up and solving 2 nonlinear equations (Newton's Law of Cooling)

Hey Dreamshot.

For number 4, you should have something like this:

(1) 34.5 = (37/2)*e^(-k(t+1)) + 16

(2) 33.7 = (37/2)*e^(-kt) + 16

Maple should solve these equations instead of the ones you gave.

Can you explain how you got your equations for number 4?

Re: Setting up and solving 2 nonlinear equations (Newton's Law of Cooling)

$\displaystyle T(t)=\text{T0}+c e^{-k t}$

solve to obtain:

c=31.445

k=0.044206

then:

T(death)=37 -> t_death=9.1327