A certain element has a half life of 4.5 billion years. a. You find a rock containing a mixture of the element and lead. You determine that 30% of the original element remains; the other 70% decayed into lead. How old is the rock? b. Analysis of another rock shows that it contains 5555% of its original element; the other 4545% decayed into lead. How old is the rock? Solution Decay constant = 0.693/half life = 0.693/4.5 = 0.154 So element has decayed to 30 % So, A(t) = Aoe^(-kt) 0.3 = 1*e^(-0.154t) take log on both sides: ln(0.3)= -0.154t t = 7.81 billion years Rock is 7.81 billion year old b) Remaining element = 55% So, 0.55 = 1e^(-0.154t) take log on both sides: ln0.55 = -0.154t t = 3.88 billion years Rock is 3.88 billion year old.