Starting with equation:
develop an analytic expression for the function,
Note: you cannot solve the first equation for Xw explicitly. Therefore you should plot the first equation listed above as Xw versus PF/PS and use any approximation to develop an expression for this function, such as using Excel to develop a trendline equation. Note that you should not use a linear approximation as this function is not linear, so pick some other function for the trendline. Ideally, you want to pick the best type of trendline function that gives the best approximation. Write down your expression for and indicate how you derived it.
Hint: Pick a reasonable range for your approximation such as 0.2< PF/PS < 2.0