Question

in a situation where the force needed to stretch a spring grows in a cubic way as the spring stretches, the force keeps increasing faster and faster.
the key feature that shows this relationship is a cubic function is that, as the spring stretches further, the force increases

Explanation:

A cubic function has the form \(y = ax^{3}+bx^{2}+cx + d\) (\(a
eq0\)). The derivative of a cubic function \(y=f(x)\) is \(y'=3ax^{2}+2bx + c\). As \(x\) (displacement in this case) increases, for \(a>0\), the derivative (rate of change of force with respect to displacement) also increases. So the force (dependent variable) increases more and more rapidly as the displacement (independent variable) increases.

Answer:

more and more rapidly