The mineral potassium, whose chemical symbol is K, is the eighth most abundant element in the earth's crust, making up about 2% of it by weight, and one of its naturally occurring isotopes, K410, is radioactive. The radioactive delay of K40 is more complex than that of carbon14 because each of its atoms decays through one of two different substances: the mineral calcium40 {Ca co), what percentage of the K-40 originally present in the sample decays to Ar-40 and what percentage decays to Ca-40? 4. Show that the age t of the rock as a function of the present amounts P(t) of K-40 and A(t) of radiogenic Ar-40 in the sample is 1 In A(t) KA + kc t = KA + ko P(t) + 1. KA 5. Suppose it is found that each gram of a rock sample contains 8.6 x 10-7 grams of radiogenic Ar-40 and 5.3 x 10- of K-40. How old is the rock