7.1 Exercise 30

Engineers desire to model the magnitude of the elastic force of a bungee cord using the equation
$F \left(x\right) = a \left[\frac{x + 9 \text{m}}{9 \text{m}} - \left(\frac{9 \text{m}}{x + 9 \text{m}}\right)^{2}\right]$,
where x is the stretch of the cord along its length and a is a constant. If it takes 22.0 kJ of work to stretch the cord by 16.7 m, determine the value of the constant a.