The parameters in equations such as these have two roles
They convert quantities from one type to another
They permit adjustments to fit observations
I can explain most easily using the parameter . The length of time until the child asks ``Are we there yet?'' increases with the number of activities A. However, we need to convert from activities to time, and does this. For example, could be 30 minutes per activity. In this case if A=2 activities, then A=60 minutes. We've gone from the number of activities to minutes.
Of course it may be that 30 minutes per activity is not the correct number. Maybe 60 minutes per activity or perhaps only 10 minutes per activity is correct. By using a parameter , a symbol rather than an actual number, we can adjust what the equation predicts by just changing the value of .
If you like, you can think of as a number we do not know, but that we could know if we made some observations.
The parameter also plays the same two roles.
What I say above is only approximately correct. I believe that it is probably sufficient to understand the basic role of the parameters in the equation. I state here the exact units for the two parameters.
converts number of activities to a pure number, so that it can be added to the pure number 1. It can be thought of as having the units of 1/activities.
converts number of children squared to inverse time. It has the units of 1/(children squared time). The time unit contained in determines what time until we add to to obtain T, e.g. could be measured in 1/(children squared hours)