You are dating Moon rocks based on their proportions of uran

You are dating Moon rocks based on their proportions of uranium-238 (half-life of about 4.5 billion years) and its ultimate decay product, lead.Find the age for a rock for which you determine that 67% of the original uranium-238 remains, while the other 33% has decayed into lead.

Solution

A = P*(1/2)^(t/4.5*10^9)

A = 0.67 P

0.67 P = P(1/2)^(t/4.5*10^9)

t = 2.6*10^9

so the rock is 2.6 billion years old