Develop a mathematical model to represent the temperature change in a water kettle over time, with the goal of identifying when the kettle is turned off. Consider factors like initial water temperature, heating element power, and insulation. Provide a step$-$by$-$step explanation of your mathematical approach and any assumptions made. Discuss potential limitations and sources of error in your model, addressing how variations in initial temperature and heating element efficiency might impact predictions. Keep your presentation clear and concise.

Perform the experiment using your home kettle.

Develop the mathematical model.

Solve the model analytically and using SIMULINK.

Compare the experimental results, analytical and Simulink solutions.