# 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 a^{0}
4.6 = C a^{1}

^{}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.