Half Life Question in Algebra

Question

living organisms have a steady amount of carbon 14 in their tissue. Once it dies the carbon 14 begins to decay. An archeologist finds bone material of what appears to be a human leg. She thinks it is 10,000 years old. If carbon 14 has a half life of 5730 what percent of carbon 14 should she expect to find in the bone?

Answer 1

Fraction left = (1/2)^(10,000/5,730)

= 0.2982924364 (approximated to 20 decimal places)

or 29.83% as a percent.

Answer 2

The formula for radioactive decay is given by: (t) = N₀​(1\2)^t\T

where:

N(t) is the remaining quantity of the substance after time t,

N₀ is the initial quantity,

T is the half-life of the substance.

In this case, the bone is assumed to be 10,000 years old, and the half-life of carbon-14 is 5730 years. So, N₀​ is the initial amount, T is the half-life, and t is the time.

Let's calculate the remaining percentage of carbon-14 in the bone:

Percent remaining=(N(t)/​N₀​)×100

Percent remaining=(1/2)^10000/5730 ​×100

Calculating this will give you the percentage of carbon-14 remaining in the bone after 10,000 years.

Hope so It will help you

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