The burial cloth of an Egyptian mummy is estimated to contain 57% of the carbon-14 it contained originally. How long ago was the mummy buried? (The half-life of carbon-14 is 5730 years.)
Solve this equation:
(1/2)^(y/5730) = 0.57
y is the age in years.
Hint: take the log of both sides (to any base), and solve for y/5730.
y = 4650 years (rounded off)
To determine how long ago the mummy was buried, we can use the concept of half-life to calculate the age.
The half-life of carbon-14 is 5730 years, which means that after 5730 years, half of the carbon-14 in a sample will have decayed. In this case, we know that the burial cloth contains 57% of the original carbon-14, so we need to calculate how many half-lives have passed based on this remaining amount.
Let's start by assuming that the original amount of carbon-14 in the burial cloth was 100%. After one half-life of 5730 years, the carbon-14 would have decayed to 50%. If the cloth now contains 57% of the original carbon-14, it means that 50% of the original carbon-14 corresponds to 57% of the remaining carbon-14.
To find the number of half-lives, we can use the formula:
N = (log(R/P)) / (log(1/2))
where N is the number of half-lives, R is the remaining amount (57%), and P is the initial percentage (50%).
Plugging in the values, we have:
N = (log(0.57/0.5)) / (log(1/2))
Calculating this expression, we find:
N = 0.0866
Now, we can find the time in years by multiplying the number of half-lives (N) by the half-life of carbon-14 (5730 years):
Time = N * half-life = 0.0866 * 5730
Calculating this expression, we find:
Time ≈ 496 years
Therefore, based on the given information, the mummy was buried approximately 496 years ago.