To find out how long ago the person died, we need to find the value of x when f(x) is equal to two-fifths (2/5) of the initial amount, A0.
We can set up the equation:
2/5 = A0 * e^(-0.0001216x)
Let's solve for x:
2/5 = e^(-0.0001216x)
To solve for x, we can take the natural logarithm of both sides of the equation:
ln(2/5) = ln(e^(-0.0001216x))
Using the properties of logarithms, we can bring down the exponent:
ln(2/5) = -0.0001216x
Now, we can isolate x:
x = (ln(2/5))/(-0.0001216)
Using a calculator, we can evaluate the right side to find:
x ≈ 11476.7 years
Therefore, the person died approximately 11,476.7 years ago.
Carbon-14 is a radioactive form of carbon that is found in all living plants and animals. After a plant or animal dies, the radiocarbon disintegrates. Scientists determine the age of the remains by comparing the amount of carbon-14 present with the amount found in living plants and animals. The amount of carbon-14 present after x years is modeled by the exponential function f(x)=A0e−0.0001216x, where A0 represents the initial amount.
Suppose a mummy from a certain country is discovered in which the amount of carbon-14 present is only about two-fifths the amount found in living human beings. About how long ago did the person die?
1 answer