The complete question is:
A certain element has a half life of 4.5 billion years.
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?
Answer:
Age of rock = 7.82 billion years
Explanation:
For a first order decay, fraction remaining is given by the formula 0.5n where n = number of half lives elapsed.
We are given that;
fraction remaining = 30% = 0.3
Thus;
0.3 = 0.5n
To find n, we have to use the log function;
log 0.3 = n log 0.5
-0.5229 = -0.301 n
n = -0.5229/-0.301
n = 1.737
We are given that;
Half life = 4.5 billion years
So, 1.737 half lives would give;
1.737 × 4.5 = 7.82 billion years
So, age of rock = 7.82 billion years