Question

Geologists can estimate the age of rocks by their uranium-238 content. The uranium is incorporated in the rock as it hardens and then decays with first-order kinetics and a half-life of 4.5 billion years. A rock is found to contain 82.7% of the amount of uranium-238 that it contained when it was formed. (The amount that the rock contained when it was formed can be deduced from the presence of the decay products of U−238.)

How old is the rock in years?

Answer 1

k = 0.693/t1/2
ln(No/N) = kt
No = 100
N = 65.7
k from above.
solve for t in years.

I found this equations, but my question is what is k?

Answer 2

k is from your first line. You know half-life is 4.5E9 yrs so you can calculate k.
N however is not 65.7 but 82.7

Answer 3

Yes, I just copied the equation off of a different problem.

Thank you for your help!