Suppose you found a material in which 12.5% of the original radioactive atoms were present. if the half-life is 47 years, how old is the material?

The answer is 141 years old.

It can be calculated using the equation: (1/2) ⁿ = x

x - decimal amount remaining,

n - number of half-lives.

x = 12.5% = 12.5%/100% = 0.125

n = ?

(1/2) ⁿ = 0.125

log ((1/2) ⁿ) = log (0.125)

n * log (1/2) = log (0.125)

n = log (0.125) / log (1/2) = log (0.125) / log (0.50) = - 0.903 / - 0.301 = 3

Number of half-lives is 3.

Number of half-lives (n) is quotient of total time elapsed (t) and length of half-life (H).

n = t/H

t = n * H

n = 3

H = 47 years

t = 3 * 47 years = 141 years

3 half lives, 141 years

(one half life: 50% left,

two half lives: 25% left;

3 half lives: 12.5% left)