The half-life of radioactive carbon-14 is 5,700 years. How much of an initial sample will remain after 4,000 years? (Round your answer to one decimal place.)

Answer 1

Let A(t) = amount remaining after t years

A(t) = Pe^kt, where P = initial amount

0.5P = Pe^5700k

0.5 = e^5700k

So, ln(0.5) = 5700k. Therefore, k ≈ -0.00012.

A(t) = Pe^-0.00012t

A(4000) = Pe^-0.48 ≈ 0.619P

About 61.9% of the original sample remains after 4000 years.