A stock trades for $$44$ per share, A call option on that stock has a strike price of $$50$ and an expiration date $6$ months in the future. When the volatility of the stock's returns is $30\%,$ the Black and Scholes value of the option is $$3\mathrm{.}82.$ Now assume, the volatility of the stock's returns is $56\%$ and the risk$-$free rate is $6\%.$ What is the Black and Scholes vlaue for this call option? By how much does the call price change?