Write down an interpretation of the function $M(G, i, t, y) = G+\frac{(i)^{\alpha}(t)^{\beta}}{y^{\delta}}$

Question

Suppose that the marks $(M)$ you get on an university exam is predicted by the following function: $M(G, i, t, y) = G+\frac{(i)^{\alpha}(t)^{\beta}}{y^{\delta}}$, where: $G$ is your current university average; $i$ is your IQ level (i.e. your intelligence); $t$ is the amount of time you spend studying for the exam; y is the year-level of the course you are taking. The values of the exponents are: $a > 1,0 < \beta <1$, and $\delta >1$ Write down an interpretation of the function in $(M)$.

Answer 1

I see its definition rather logical, because you start of your past achivement traduced by constant $G$ (initial condition) in the three-dimensional space described by $(i,t,y)$.

Then when your Qi is high (even if it is in reality discutable) you're disposed to get higher mark, hence the proportionnality with the terms $i^\alpha$ (note that $\alpha$ is positive, hence the direct proportionality)

Same for the time the more you work, the more you are supposed to get $\beta$ also positive.

For $y$ there are two equivalent interpretation (depending on what parameter you fix).

If you're in higher graded teaching you've to work more (so increase $t$) or be more 'intelligent' (increase $i$) this is traduced by the fraction.

The second interpretation is, for a fixed mark $M$ and others fixed parameters, it is harder to get an higher mark in high graded year.

$\gamma$ is also defined positive.

Finally $\alpha,\beta,\gamma$ are parameters depending on the person. (even for QI, two persons with the same will not act similarly).