Consider a spherical rubber balloon with an uninflated radius $R.$ The internal air pressure $p$ to inflate the balloon as a function of the radius $r$ is given by the pressure curve:

$p=\frac{C}{r{R}^2}[1-(\frac{R}{r}{)}^6]$

Here, $C$ is a material property describing the energy required to inflate the balloon for a specific rubber and temperature. Let $R=0\mathrm{.}02m$ and $C=0\mathrm{.}026J.$

a$)$ Use the bisection method $($You can do it in a spreadsheet or by hand calculation$)$ in the interval $[a,b]=[0\mathrm{.}03,0\mathrm{.}06]$ with a tolerance $={10}^{-4}$ to estimate the balloon radius $(r)$ for a pressure $p=1400P.$ Decide the convergence criterion and comment on it$.$