Question

The level of thorium in a sample decreases by a factor of one-half every 4.2 million years. A meteorite is discovered to have only 7.6% of its original thorium remaining. How old is the meteorite?

Answer 1

15.6 million years

Explanation:

Let us write the expression as follows:
`(1/2)^N=7.6%`
N being the number of half times passed,

Since after each half life, the value is halved.

Now that we have the unknown, number of half lives passed in the power, we will use log formulas:
`if a^x=b," then "x=log_ab`
`log_ab=logb/loga`

In our case:
`(1/2)^N=7.6%=7.6/100=0.076`
`(1/2)^N=0.076`
`N=log_(1/2)0.076=log0.076/log(1/2) ≈3.72`

To get number of years (how old) we have to multiply the number of half-live passed by the number of years each half life takes:
`age=N*4.2 million=3.72*4,200,000= 15,614,9981 ≈15.6 million`