In the year 2005, a picture supposedly painted by a famous artist some time after 1815 but before 1865 contains 95 percent of its carbon-14 (half-life 5730 years).
Approximately how old is the painting? years
just solve for t in
(1/2)^(t/5730) = 0.95
To determine the age of the painting, we can use the concept of carbon dating and the known half-life of carbon-14. Carbon-14 is a radioactive isotope of carbon that decays over time. By measuring the amount of carbon-14 remaining in a sample, we can estimate its age.
Given that the painting contains 95 percent of its carbon-14, this means that only 5 percent of the original carbon-14 has decayed.
To calculate the number of half-lives that have passed, we can use the formula:
(number of half-lives) = (log of remaining carbon-14) / (log of 0.5)
Using the equation, we can solve for the number of half-lives:
(number of half-lives) = log(0.05) / log(0.5)
Now, we know that the half-life of carbon-14 is approximately 5730 years. By multiplying the number of half-lives by the length of each half-life, we can estimate the age of the painting:
Age of the painting = (number of half-lives) * (length of each half-life)
Now, let's calculate the age of the painting:
(number of half-lives) = log(0.05) / log(0.5) ≈ 3.86
Age of the painting ≈ (3.86) * (5730 years) ≈ 22,152 years
Therefore, the painting is approximately 22,152 years old.