CT,  prolly in some civil/mechanical engineering problem. i am guessing--- some dam/turbine problem. but i don't know for sure. i am just interested in the mathematical bit.

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yes khaobadi. that is exactly what i am saying, equal percentage flow for equal increment in valve opening.

but that example gives '59.something' percentage change in the first case and '61. something' percentage change in the second. i am sure, there is ought to be some tolerance, but that's just a tad bit big IMO. I am not sure if its tolerable for this particular problem (mechanical/civil)

and your second example of your first post gives '36.6' percentage' initially and '56.something' later on.

parbatya's solution also gives range of percentage change -- from 33% to 60%

i am thinking, there are other requirements to this problem (for it to be complete so as to get a unique answer). else, there could be myriad solutions and values for the constants --none of them giving a perfect equal percentage solution.

or it could just be that he wanted to draw just a close-to-accurate graph and that's it.

let's hear more from v2001.