GeoGebra Kennslustofan

# Proposed solution 2

## Suspect

Did the language teacher, Nicci Vulture, stab the mathematics teacher from behind with a papercutter …? Is that even possible? With a nagging feeling that something is not completely right, you slowly walk back into the school building and to the principal’s office to report your conclusions to your chief. It is a little bit warmer inside than outside and a shiver runs down your back. You take a few deep breaths and try to calm down. Your conclusions are surely on target…

## Aha!

On your way to the principal’s office, it suddenly strikes you. The temperature outdoors is falling! At 9 o’clock it was 25°C, at 10 o’clock it was just 22°C, and now—at almost 11 o’clock—the temperature is down to about 20.5°C. Your model is wrong, but how do you find a model that takes into account an outdoor temperature that is falling? You will have to solve the basic differential equation again. Of course, it wasn’t the language teacher Nicci Vulture, 77 years old, who killed the mathematics teacher, you think while you are finishing off your new calculations. It must have been … You search in the list of the suspects. How strange… Who did kill the mathematics teacher?

## Let us continue...

The temperature is falling at 3°C per hour since at least 8:30 that morning. Newton’s cooling law claims that the speed of cooling is proportional to the difference in temperature. You therefore set up the differential equation `T′ = k · (T – (22 – 3t))`, where the time t once again is measured in hours after 10:00. Open up the GeoGebra CAS window from the menu Show > CAS and type

`SolveODE[y′ = k(y – (22 – 3x))]`

You find that y = (c1 k ekx – 3kx + 22k – 3)/k = c1ekx – 3x + 22 – 3/k. Now you create a new model function

`m2(x) = c e^(k x) – 3x + 22 – 3/k`

You allow GeoGebra to create the necessary sliders and then fit a function of this type to the data, using

`Fit[{A,B}, m2]`

Who killed the mathematics teacher?