what factor does the amount of mechanical energy stored in the spring change?

Question

A spring is stretched by an initial amount from its relaxed state. If the spring is then stretched by three times that amount from its relaxed state, by what factor does the amount of mechanical energy stored in the spring change?

PEfinal

PEinitial

Answer 1

the correct answer is it goes up by a factor of 81.

Answer 2

The energy goes up by a factor of 9.

The reason is that energy of a spring depends on the square of the displacement:

E = kx²/2