Answer: We can use the formula for radioactive decay:
N = N0 * (1/2)^(t/T)
where N is the current amount of the radioactive substance, N0 is the original amount, t is the time that has passed, T is the half-life.
Let's assume that the original amount of the substance in the rock was 8 units. If the current amount is 1 unit, then:
1 = 8 * (1/2)^(t/1.5 billion)
Taking the natural logarithm of both sides, we get:
ln(1) = ln(8) - (t/1.5 billion)*ln(2)
Simplifying:
0 = ln(8) - (t/1.5 billion)*ln(2)
t/1.5 billion = ln(8)/ln(2)
t = 1.5 billion * (ln(8)/ln(2))
t ≈ 3.91 billion years
Therefore, the moon rock is about 3.91 billion years old.
Explanation: