A mummy discovered in Egypt has lost 46% of its carbon-14. Determine its age.
If the half-life is n years, then solve for n:
(1/2)^n = .54
Oops. Make that
(1/2)^(t/n) = .54
and solve for t
looks like it should be just under 1 half-life
Sorry, the equation that is given in the book is y=y_0e^-.0001216t
To determine the age of the mummy, we can use the concept of half-life of carbon-14.
The half-life of carbon-14 is about 5730 years, which means that every 5730 years, the amount of carbon-14 in a sample reduces by half.
Given that the mummy has lost 46% of its carbon-14, it means that it has only 54% of the original amount remaining.
To find the age of the mummy, we can use the formula:
Age = (number of half-lives) * (half-life of carbon-14)
First, we need to determine the number of half-lives by finding the ratio of the remaining carbon-14 to the original amount. Since the mummy has 54% of the original carbon-14 remaining, the ratio is 0.54.
Now, we can calculate the number of half-lives:
log(0.54) / log(0.5) ≈ 0.425
Next, we multiply the number of half-lives by the half-life of carbon-14:
Age ≈ 0.425 * 5730 years ≈ 2437 years
Therefore, the approximate age of the mummy is 2437 years.