The half-life of Carbon 14 is 5700 years. A wooden table is measured with 80% of Carbon 14 compared with newly cut tree. Find the age of the table.

Question

Quizplus · Accepted Answer

Using the formula for exponential decay: 
(amount remaining) = (initial amount) x (1/2)^(time/half-life)
Let t be the age of the table, then we have:
0.8 = 1 x (1/2)^(t/5700)
Taking the logarithm of both sides:
log(0.8) = log(1/2)^(t/5700)
log(0.8) = (t/5700) x log(1/2)
t/5700 = log(0.8) / log(1/2)
t/5700 = 0.322
t = 5700 x 0.322
t = 1835.4 years
Therefore, the age of the table is approximately 1,835 years. The best choice is letter G.

The Half-Life of Carbon 14 Is 5700 Years