Why rocket altitude does not increase proportionally?

[Starnair]

Homework Statement

1. Why rocket altitude does not increase proportionally with the amount of rubber band stretch? Provide an explanation for the lack of direct correlation.
I'm not sure that I am doing in right way, and cannot understand why k value is decreasing as rubber band stretches because I thought k value never changes.

Relevant Equations

Es=Eg
Photo includes this.

I thought it is because of the consevation of the energy, so I used (gravitational potential energy at the top = elastic potential energy). Since the mass of the rocket never changes, I supposed mass= 1kg, and k value is unknown. As a result, I got the result that k value is decreasing as ruvber band stretches.

 

[phinds]

I don't think your attachment would be legible even if you had NOT posted it sideways. You should fix both of those issues and re-post it.