POSSIBLE SOLUTION(S)

1) Fit the hill side data to a 3rd degree polynomial of the form
y = A x^3 + B x^2 + C x + D.
Does this offer a reasonable fit?
You'll use this path equation to answer the rest of the questions.

Input := 

Path[x_] = Fit[PathData, {1, x, x^2, x^3}, x]

Output =

                                    2                 3
49.4685 - 0.0274281 x - 0.00344406 x  + 0.0000117521 x

Input := 

p2 = Plot[Path[x], {x, 0, 200},
	DisplayFunction -> Identity]

Output =

-Graphics-

Input := 

Show[p1, p2, DisplayFunction -> $DisplayFunction]

Output =

-Graphics-

By visualization, the fit looks pretty good!

2) How many steps are necessary, and what are their individual lengths, i.e. tread lengths? (You'll have to build a table since each step will likely have a unique tread length.)

3) How long is the paved section of the path? (Be sure to give the true length -- not the horizontal length.)

Input := 

PaveLength =
	NIntegrate[Sqrt[1+(Path'[x])^2], {x, 0, x1}] +
	NIntegrate[Sqrt[1+(Path'[x])^2], {x, x2, 200}]

Output =

144.572

4) The cost of paving is $2.00 per square foot and the cost of putting in steps is $2.50 per square foot (horizontal area only). How much will the path cost to build?

Input := 

PaveCost = 4 2 PaveLength

Output =

1156.58

Input := 

StepCost = 4 2.5 StepLength

Output =

604.085

Input := 

Cost = PaveCost + StepCost

Output =

1760.66

So, the total cost is $1760.66.