Cans experiment and Newton's Law of Cooling

We did the experiment where you pour boiling water into a black tin and a shiny tin and let them cool. I had never thought about the equation of the curve but guessed it was exponential. It turns out that it follows Newton's Law of Cooling. The rate of fall of temperature is proportional to the temperature difference between inside and outside the can. In other words, a hot can cools faster. The solution is an exponential equation. https://www.ugrad.math.ubc.ca/coursedoc/math100/notes/diffeqs/cool.html I used the experimental data to plot LN graphs to get the factor k from the gradient. I did it for both black and shiny tins:

Having got the values for k, I put them back into the equation from the linked page and got the theoretical cooling curves if we had done the experiment for an hour.