How many years would it take a 2000 gram sample to decay to only 400 grams?

Question

The rate of decay for a particular type of radioactive particle is relatively constant, and can be represented using the equation (- In 2) N (t) = Nee 3 Where t is time, N is the mass of the sample, and is the half-life (time it takes for half of the initial sample to decay). The half-life of Carbon-14 is about 5730 years. How many years would it take a 2000 gram sample to decay to only 400 grams? Round your answer to the nearest tenth.

Answer 1

in 5730 years 2,000 decays to 1,000

in 11,460 years 2,000 decays to 500

in 17,190 years 2,000 decays to 250

somewhere betwen 11,460 and 17,190 years, 2000 decays to 400 grams

2000=40(2)^h

5 = 2^h

h = about 2.322 half lives

2.322 x 5730 = about 13,305.1 years to decay to 400 grams