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 iE? = udt + odW(t) for a standard Brownian motion and real value p and o > 0. Now, let U(t) = $ be the exchange rate of euro against the dollar. Show that U(t) satisfies the following stochastic differential equation. dU(t) (1(t) = (02 u)dt adWOE)