Let S(t) be the price of dollar at time t, i.e. the number of euros per dollar. The behavior of S(t) through time is modeled by dS(t)/S(t) = mu dt + sigma dW(t) for a standard Brownian motion and real value mu and sigma > 0. Now, let U(t) = 1/S(t) be the exchange rate of euro against the dollar. Show that U(t) satisfies the following stochastic differential equation. dU(t)/U(t) = (sigma^2 - mu) dt - sigma dW(t)