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?

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?

Age of rock = 7.82 billion years

Step-by-step 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

relating to or denoting a system of numbers and arithmetic based on the number ten, tenth parts, and powers of ten.

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