Ok this mathematical situation has bugged me all day (I am a high school math teacher) so I broke out my skills eventhough I am on break.
1) jon's theory was based on the eye test saying marble's skills have grown exponentially not his points (I believe...correct me if I'm wrong).
2) numbers were thrown out to go over the difference between the two types being exponential vs linear. Those numbers had nothing to do with marble's actual points so they were only to show what someone was talking about.
3) linear growth is growth by a constant number. Where as exponential growth is a growth factor based off of percentage. In exponential growth you have a formula of y=a*b^x...so if b is 1.4 you are growing at 40% or if b is 2 you are growing by 100%. Linear growth formula is y=a+bx or y=mx+b (latter is the u.s. version) where if the b or m (number multiplied by x) is 1.4 you go up by 1.4 each time.
4) so I graphed the data and did regressions to find the closest fits. I used x of 0, 1, 2 (frosh, soph, jr) and y of 5.7, 11.5, 16.1 (his points average for each yr). Neither equation linear or exponential was a great fit. When graphing the data you see a definite curve but it isn't exponential as the percent growth is decreasing each time. The linear equation actually fit better than the exponential.
5) exponential equation - y=6.06*1.68^x...this gave the following
Freshman yr - 6.06 ppg (+0.36 points from actual)
Sophomore yr - 10.181 ppg (-1.319 points from actual)
Junior yr - 17.104 (+1.004 points from actual)
Senior prediction - 28.734 ppg
6) linear equation - y=5.2x+5.9...this gave the following
Freshman yr - 5.9 ppg (+0.2 points from actual)
Sophomore yr - 11.1 ppg (-0.4 points from actual)
Junior yr - 16.3 ppg (+0.2 points from actual)
Senior prediction - 21.5 ppg
7) the numbers seem to say more like linear growth and the 21.5 ppg prediction sounds much more feasible.
8) but based off the eye test and not the numbers marble's skills do seem to have grown exponentially.
Sorry if this was confusing but I had to get it off my chest as many people just throwing out random stuff that wasn't even numbers associated with devyn's growth.