Q(t)=q(0)e^pt
the above model describes the exponential decay of chemical element. t is the time in years, q(0) is the initial amount of the chemical element, q(t) is the amount of chemical element after t years and p is a constant. it is known that every 1600 years the amount of the chemical element drops to half ( its half-life is 1600 years). if the term e^p in the above equation can be replaced by the term x^y, where both x, y rational numbers, what is x and y?

(a) x=sqrt{frac{1}{2}}, y=frac{1}{1600}

(b) x=frac{1}{2}, y=frac{1600}{3}