Problem 1- Calculate the amount of ¹⁴C remaining in a sample.

Suppose an organism has 20 g of ¹⁴C at its time of death. Approximately how much ¹⁴C remains after 10,320 years?

Tutorial

Using the above model, N(t) = N₀ e ^{−0.0001216 t}, with N₀ = 20 gives,

N(t) = 20 e ^{-0.0001216 t}.

To find the amount of ¹⁴C remaining after 10,320 years, substitute t =10,320 into the above equation,

N(10320) = 20 e ^{(−0.0001216)·(10320)} ≈ 5.7.

Thus, an initial sample containing 20 g of ¹⁴C contains approximately 5.7 g after 10,320 years.

This answer makes sense because the half-life of ¹⁴C is 5700 years, meaning there would be 10 g left after 5700 years and 5 g after 11,400 years.