Question

An archaeologist found the bones of a primate. She found that 2.5% of the Carbon-14 that it

would have had when it was alive remained. Estimate the age of the bones using the formula:
y =ae-0.000123 .

Answer 1

The age of primate bones with 2.5% of Carbon-14 remaining is estimated using the decay formula and the half-life of C-14. By using the given formula and solving for 't', the bones are determined to be approximately 29,271 years old.

Step-by-step explanation:

To estimate the age of primate bones, in which 2.5% of Carbon-14 (C-14) remains, we use the decay formula relating to the half-life of C-14. The half-life of C-14 is approximately 5730 years. The decay formula is y = ae-0.000121t, where 'y' is the remaining amount of C-14, 'a' is the initial amount of C-14, and 't' is the time in years since the organism died.

To solve for the age, we rearrange the formula to solve for 't', taking natural logs if necessary. With 2.5% of C-14 remaining, we can calculate the age as follows:

t = (ln(y/a))/(-0.000121)

t = (ln(0.025))/( -0.000121)

t = ln(0.025) / -0.000121

t ≈ 29271 years

Therefore, the estimated age of the primate bones is approximately 29,271 years old.