Proposed solution 1
- Author:
- Bea Kristinsdóttir
Newton's law of cooling
Select the variables so that you measure the time from 10:00 a.m. and the surrounding
temperature, which is 22°C. Newton’s law of cooling:
tells that the body temperature will change proportionally to the difference between the body temperature and the surrounding temperature.
Try setting up equations and fitting a model to the data. An example of how this is done is shown below.
Try it out:
Solution example
This will yield the following system of equations:
You can add the lines
8.3 = C a0 4.6 = C a1
You can solve the system of linear equations in different ways. Here is a suggestion:| 1. | In the input line create two points A = (0 , 30.3)
and B = (1 , 26.6)
|
| 2. | Write the model function in the input line m(x) = p q^x + 22 |
| 3. | Adjust the model with the sliders to go close to or through the points A and B before you hide m and type in the input line Fit[{A,B}, m] |
y = 22 and y = 36.8 to indicate the temperature of the surroundings and the body temperature.