A whalebone that originally contained 212 grams of C-14, half-life of 5700 years, now contains only 53 grams of C-14. How old is the whale bone?

A) 2850 years

B) 5700 years

C) 11400 years

D) 17100 years

The answer is C) 11400 years

Let's first calculate the remaining amount in percent:

212g is original amount or 100%.

53 g is x percents.

212 g : 100% = 53 g : x

x = 100% * 53 g : 212 g

x = 25% = 0.25

Now, using the formula to calculate the number of half-lives:

(1/2) ⁿ = x,

where

x is the remaining amount: x = 0.25

n is the number of half-lives

1/2 stands for half-life.

(1/2) ⁿ = 0.25

⇒ n*log (1/2) = log (0.25)

n = log (0.25) / log (1/2) = log (0.25) / log (0.5) = - 0.602/-0.301 = 2

The number of half-lives is 2.

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

L = 5700 years

T = ?

Thus

T = L * n

L = 5700 years * 2

L = 11400 years