Implied Volatility by Bisection

Implement implied_vol(price, S, K, T, r) that returns the Black–Scholes implied volatility of a European call (no dividends) given its market price.

Use a robust root-finding method. The Black–Scholes call price is strictly increasing in $\sigma$, so bisection on $\sigma \in [10^{-6}, 5]$ always converges when a solution exists. Return a float accurate to within $10^{-4}$.

A helper bs_call is provided in the starter code.