I'm trying to model a 3D surface which reflects the solubility of $CO_2$ in beer. An empirically derived chart is available at this link.
Solubility is empirically related to the pressure of $CO_2$ in the space above the beer and to temperature. Solubility is directly and linearly related to the pressure (Henry's Law). Solubility is exponentially related to the temperature of the beer (Van't Hoff).
I intend to use python's scipy's curve_fit (with a custom function) to minimize the least-squares difference between my model and the data in the chart.
I am assuming the following relationships between solubility, pressure, and temperature:
With respect to pressure,
$$solubility(pressure) = m \times pressure + b$$
With respect to temperature,
$$solubility(temperature) = C+A\times e^{(B\times temperature)}$$
My question is this: what should my custom estimating function look like? $$solubility(pressure,temperature) = ???$$