Tests of an artifact discovered at the Debert site in Nova Scotia show that 28% of the original C14 is still present. Approximately how old is the artifact?

Question

28% = 7/25

(7/25)P = Pe^(-5730k)
(ln(7/25))/(-5730) = k
2.22 x 10^-4 = k

(7/25)P = Pe^(-kt)
(ln(7/25))/(-k) = t
5 730 years = t

... my answer is wrong and the textbook answer is 10,523 years. Please help?

Answer 1

Well, half is gone in 5730 years, and 3/4 will be gone in 2x5730, so I know your answer is wrong.
.28=1e^(-kt/5730) k=.692
5730ln .28= -.693t
solve for t.