The half life of pb-210 is 22 years. a decayed animal shows 16% of the original pb-210 remains; how long has the animal been deceased to the nearest tenth of a year?

The answer is 8.5 years

Let's use the formula to calculate the number of half-lives:
(1/2)ⁿ = x,
where
x is the remaining amount in decimals: x = 16% = 0.16
n is the number of half-lives
1/2 stands for half-life.
(1/2)ⁿ = 0.16
⇒ n*log(1/2) = log(0.16) 
    n = log(0.16)/log(1/2) = log(0.16)/log(0.5) = -0.796/-0.301 ≈ 2.6
The number of half-lives is 2.6.

Now, the number of half-lives (n) is a quotient of total time elapsed (T) and length of half-life (L):
n = T/L
We know:
n = 2.6
T = 22 years
L = ?
Thus
L = T/n
L = 22 years/2.6 = 8.5 years

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