4. Find a polynomial function which fits this data.

After experimenting with various polynomials, a seventh degree polynomial gives a reasonable shape for the curve including extreme values and concavity.

Input := 

f[x_]= Fit[thePoints,{1,x,x^2,x^3,x^4,x^5,x^6,x^7}, x]

Output =

                                  2
0.00780109 + 2.18079 x - 393.385 x  + 
 
           3             6  4
  127454. x  - 3.64084 10  x  + 
 
            7  5             8  6
  4.07979 10  x  - 1.99528 10  x  + 
 
            8  7
  3.54337 10  x

Input := 

fPlot = Plot[f[x],{x,0,.19},
	AxesLabel -> {TIME, POWER}, 
	PlotLabel -> BattingPower,
	DisplayFunction -> Identity];

Input := 

Show[fPlot, s,
	DisplayFunction -> $DisplayFunction]

Output =

-Graphics-