I'm having trouble understanding how to model this through a phase shift. Essentially, I'm modelling a cooling curve through:
$$T(t)= (T_o - T_a)*e^{-kt} + T_a$$
$K$ is the gradient of the line, $T_o$ is the initial temperature and $T_a$ is the ambient temperature. Now, If I model the data from the graph, you will see there's a massive drop between $t = 8$ and $t = 10$. This is because milk is added. So, what I'm trying to do is fit a trendline to extract a formula:
[All values have ambient temperature subtracted because having the +24 screws with excel as it tries to reach this ambient temp, screwing with the trendline.]
Notice how inaccurate the exponential function is. Apparently I can use a phase shift, yet I've tried this on desmos and it hasn't helped me yet...
If I use this formula and just add +24 to every value, the data set is extremely off. For example, at $t=2$ I get 61 instead of 74.5.
So what else could I do?