Cosmic-ray bombardment of the atmosphere produces neutrons, which in turn react with nitrogen to produce radioactive carbon-14 (¹⁴C). Radioactive ¹⁴C enters all living tissues through carbon dioxide, which is first absorbed by plants. As long as a plant or animal is alive, ¹⁴C is maintained in the living organism at a constant level. Once the organism dies, however, 14C decays according to the equation

where A is the amount present after t years and A₀ is the amount present at time t = 0.

(A) If 500 milligrams of ¹⁴C is present in a sample from a skull at the time of death, how many milligrams will be present in the sample in 15,000 years? Compute the answer to two decimal places.

(B) The half-life of ¹⁴C is the time t at which the amount present is one-half the mount at time t = 0. Use Figure 6 to estimate the half-life of ¹⁴C.

Transcribed Image Text:

A = Age Age-0.000124t