An artifact was found and tested for its carbon-14 content. If 77% of the original carbon-14 was still present, what is its probable age (to the nearest 100 years)? Use that carbon-14 has a half-life of 5,730 years.

Answer 1

Since this is a half-life type, we can use the base of 1/2

.77 = (1/2)^(t/5730)
ln .77 = ln (.5^(t/5730))
t/5730 = ln.77/ln .5
t = 5730(ln.77/ln.5) = 2160.6

to the nearest 100 years that would be 2200 years.

Answer 2

The atmospheric pressure P in pounds per square inch (psi) is given by the formula below, where a is the altitude above sea level (in miles). If a city has an atmospheric pressure of 13.25 psi, what is its altitude? (Recall that 1 mi = 5,280 ft. Round your answer to the nearest foot.)