Your model is a rate model because you use the temperature as your independent variable, but it's still governed by the same underlying process. I was merely trying to say that 'exponential' growth is a 'special case' of logistic growth, valid under conditions were there are no resource constraints yet. In the sense that the exponential part of your model does in fact represent something more than just being a convenient function that happens to fit the data...
Yes, exponential growth is an underlying assumption – no doubt about that – but not as you stated in your comments with respect to the specific functioning of the model. Perhaps some of the confusion is that I was not particularly clear in my original response to you that I was only talking about the specific part of the model Jim asked about – not the model as a whole.
You mischaracterized how the model functions when you responded to my comment about a specific ex
term writing “It represents exponential growth…” and you mischaracterized it again here when you stated that this specific term as used represents more than a convenient function to fit the data. It does not.
The part of the model you commented on simply describes the effect of temperature on a relative growth rate. It’s time independent, in fact, the dependant variable is dimensionless. The function in question does not represent exponential growth (which always has time as an independent variable and a dependent variable with a dimension that represents a quantity of some sort such as number of cells or cell mass).
I think you are confusing the exponential function with exponential growth. The particular term in question is simply part of a larger function that describes how yeast growth rate varies with temperature, the result of which is used in the larger model which incorporates an exponential growth assumption.