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

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

Original question:

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

Step 1:

My [correct] solution to step 1:

Step 2:

My [correct] solution to step 2:

Step 3:

My [correct] solution to step 3:

Step 4 (this is where the problems begin):

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!):

Step 5

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):

_______________

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.

2. ## 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?

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

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

solve to obtain:

c=31.445
k=0.044206

then:

T(death)=37 -> t_death=9.1327