Acertain 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 15% of the original element remains; the other 85% decayed into lead. how old is the rock? b. analysis of another rock shows that it contains 55% of its original element; the other 45% decayed into lead. how old is the rock?

Question 1 - 85% Decayed
elapsed time = half-life * [log (bgng amt / end amt)] / log (2)
elapsed time = 4.5*10^9 * [log (100 / 15)] / 0.30102999566
elapsed time = 4.5*10^9 * (0.82390874095 / 0.30102999566)
elapsed time = 4.5*10^9 * 2.7369655942
elapsed time = 12,316,345,174. Years

Unless I calculated incorrectly, or the problem is stated incorrectly, the age of the rock CAN'T be 12.3 billion years old since the Earth is about 4.5 billion years old.



Question 2 - 45% Decayed
elapsed time = half-life * [log (bgng amt / end amt)] / log (2)
elapsed time = 4.5*10^9 * [log (100 / 55)] / 0.30102999566
elapsed time = 4.5*10^9 * 0.25963731051 / 0.30102999566
elapsed time = 4.5*10^9 * 0.8624964763
elapsed time = 3,881,234,143 billion years

The answer would be 7 cages