Regression (I think) of Newton's Law of Cooling

1. Mar 13, 2012

HalcyonStorm

1. The problem statement, all variables and given/known data
Using a data logger, I have collected data for two cooling cups: the temperature (c) at 1 second intervals. My task was to model this data using two methods.

"METHOD 1: Use EXCEL or the regression analysis capability of your graphic calculator"
"METHOD 2: Find the constants in the model (A0 and k) by constructing a linear function relating lny and t."

I chose to use Excel for method 1. I have attached the spreadsheet.

2. Relevant equations
Newton's Law of Cooling: y=A0*e^kt

3. The attempt at a solution
I have attached the graphs that I have been able to produce (method 1) in a word document. I am unable to do method 2, as I'm really stuck for ideas.

Thank-you! Any help is much appreciated :)

Attached Files:

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• u1.xls
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Last edited: Mar 13, 2012
2. Mar 13, 2012

Staff: Mentor

For method 2, the idea is to find constants A0 and k for which lny = kt + A0. If you plot lny versus t, this equation represents a straight line.

3. Mar 14, 2012

HalcyonStorm

Would it be safe for me to assume that (from y= mx + c), k is equal to m and A0 is equal to c?

4. Mar 14, 2012

Staff: Mentor

Yes.

5. Mar 14, 2012

TheoMcCloskey

Be careful! - Its really "c = ln(A0)"

6. Mar 14, 2012

Staff: Mentor

No, not if the OP is working with the equation lny = kt + A0.

7. Mar 15, 2012

TheoMcCloskey

Yes, that is is correct, and I stand corrected. I was assumming the OP's original equation was, as he stated in "Relevant equations", of the form $y = A_0 \cdot e^{kt}$.