+118659 Hi rarinstraw,
Gino is really good at these he may have a better way to do it.
I set up these four equations
\(cost = ax^2+bx+c\\~\\ 550=a*225+b*15+c\\ 700=a*289+b*17+c\\ 1500=a*529+b*23+c\\ 2500=a*900+b*30+c\)
Then I solved them simultaneously.
I got
\(a\approx 3.23\\ b\approx -28.40\\ c\approx 249\\ so\\ cost\approx 3.23x^2-28.40x+249\)
https://www.desmos.com/calculator/h94xx9vjun
3.23*42^2-28.40*42+249 = 4753.92
The points do not fit on the graph exactly because the these points will not fit any quadratic model exactly.
So the estimated cost of a 42cm tele is $4754
BUT since 42cm is an extrapolated point (larger than any of the other sizes) you would need to be very careful about relying on this price.
