How old are the mastodon bones found in Austin, Texas?

Explanation:

The age of the mastodon bones can be estimated by using the concept of radioactive decay of carbon-14. Carbon-14 has a half-life of 5730 years, which means that it takes 5730 years for half of the original amount of carbon-14 to decay. In this case, only 1/64 of the original carbon-14 remained in the mastodon bones.

The formula to calculate the remaining amount of a radioactive isotope after a certain number of half-lives is:

M = M₀ × (1/2)ⁿ

Where M is the remaining amount, M₀ is the initial amount, and n is the number of half-lives elapsed.

Given that 1/64 of the original carbon-14 remained, we can set up the equation:

(1/64) = (1/2)ⁿ

By solving for n:

(1/2⁶) = (1/2ⁿ)

2⁶ = 2ⁿ

6 = n

Therefore, 6 half-lives have elapsed since the mastodon died and the remains were dated. To find the age of the mastodon bones, we need to multiply the number of half-lives by the half-life time:

6 × 5730 years = 34,380 years

So, the mastodon bones found in Austin, Texas are approximately 34,380 years old.