Carbon 14 has a life of 5,730 years. a) obtain an exponential decay model for the isotope in the form Q(t)=Qoe^-kt. Round k to four decimal places.) b.) About 500 milligrams of the isotope are produced in a certain nuclear reactor. Use your model to predict how long it will take for this amount to decay to 5 milligrams. (Round to the nearest year)