Needing an equation that describes the relationship between three variables

Question

I have three variables that have a specific relationship with each other. I know what they need to do at specific points, but I need to find out the values in between, and I need an equation that describes their interdependency.

I'll call them T, V, and X. T ranges from 0 to 100, V ranges from 0 to 40, and X ranges from 0 to 5. T and V are both needed to determine values for X.

When V is 0, X is unaffected, regardless of what T is.

When T is 50, X is unaffected, regardless of what V is.

When V is 20, X is 2.5 when T is either 0 or 100.

When V is 40, X is 5 when T is either 0 or 100.

What is the simplest equation that describes the relationship between these variables?

Answer 1

X = 1/400 × V × |T - 50|

From the first assumption, X is some function of V and T.

From the first 2 conditions, we know V(T - 50) should be in there

Since we just need the simplest relation, we can assume

X = k V(T - 50) + b

From the next two conditions, we can take the absolute value of T - 50, so it becomes

X = k V |T - 50| + b,

plug in the numbers,

X = 1/400 V |T - 50| + b.

There is not enough information to specify b, as the last two conditions have the same effects.

For simplicity, we can drop b, hence we get the relation I placed in the beginning.