Question

The radioactive element​ carbon-14 has a​ half-life of 5750 years. A scientist determined that the bones from a mastodon had lost ​60.1% of their​ carbon-14. How old were the bones at the time they were​ discovered?

please help me with this problem.....

Answer 1

Answer: To solve the problem, we can use the formula for exponential decay:

N(t) = N0 * (1/2)^(t/T)

where:

N(t) is the amount of the radioactive element at time t

N0 is the initial amount of the radioactive element

t is the time that has elapsed

T is the half-life of the radioactive element

Let's assume that the initial amount of carbon-14 in the bones was N0. After the bones were discovered, they had lost 60.1% of their carbon-14, which means that only 39.9% of the original carbon-14 remained. Therefore, we can write:

N(t) = 0.399 * N0

We want to find the time t that has elapsed since the mastodon died. We can rearrange the formula for exponential decay to solve for t:

t = T * log( N(t) / N0 ) / log(1/2)

Substituting the given values, we get:

t = 5750 * log( 0.399 ) / log(1/2)

Using a calculator, we find that t is approximately 16060 years. Therefore, the bones were approximately 16060 years old at the time they were discovered.

Explanation: