A mummy was recently discovered.  It now contains 88.8​% of its original Carbon 14.
About how old is the mummy.  Assume that the​ half-life of Carbon 14 is 5730 years.
The mummy is about how many years old

The decay of Carbon-14 follows an exponential decay model, given by the formula:

\[
N(t) = N_0 \cdot e^{-\lambda t}
\]

Where:
- \( N(t) \) is the remaining amount of Carbon-14 after time \( t \),
- \( N_0 \) is the initial amount of Carbon-14,
- \( \lambda \) is the decay constant,
- \( t \) is the time that has passed.

Since the problem states that the mummy contains 88.8% of its original Carbon-14, we can set:

\[
\frac{N(t)}{N_0} = 0.888
\]

The decay constant \( \lambda \) is related to the half-life \( T_{1/2} \) by the formula:

\[
\lambda = \frac{\ln 2}{T_{1/2}}
\]

For Carbon-14, the half-life is 5730 years, so:

\[
\lambda = \frac{\ln 2}{5730}
\]

Now, we can solve for \( t \) using the equation:

\[
0.888 = e^{-\lambda t}
\]

Taking the natural logarithm of both sides:

\[
\ln(0.888) = -\lambda t
\]

Solving for \( t \):

\[
t = \frac{-\ln(0.888)}{\lambda}
\]

Let's calculate the age of the mummy.The mummy is approximately 982 years old.

Would you like more details on the calculation, or do you have any further questions?

Here are five related questions for further exploration:

1. How would the age change if the mummy had only 50% of its original Carbon-14?
2. What is the formula for exponential decay in general?
3. How is the concept of half-life applied in fields other than archaeology?
4. How would the age of the mummy change if a different isotope with a shorter half-life was used?
5. Can Carbon-14 dating be used on objects older than 50,000 years?

**Tip:** In radiometric dating, the accuracy of age estimates depends on the preservation of the sample and the assumption that the decay rate remains constant over time.

A mummy was recently discovered. It now contains 88.8% of its original Carbon 14. About how old is the mummy? Assume that the half-life of Carbon 14 is 5730 years.

Discover how to calculate the age of a mummy using the concept of Carbon-14 decay. This detailed solution explains exponential decay, the half-life formula, and logarithmic functions to find the age of a mummy that contains 88.8% of its original Carbon-14. Suitable for Grades 10-12.

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