# Proposed solution 1

## 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.

## Solution example

This will yield the following system of equations:

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]
You can add the lines y = 22 and y = 36.8 to indicate the temperature of the surroundings and the body temperature.