# If the initial amount of Carbon-14 in the mammoth was 8 grams, how many half-lives have passed i the fossil sample has 1 gram left? How many years have passed since the mammoth's death?

## Why did the mammoth become such a hoarder? It just couldn't let go of even a single gram of Carbon-14! But I digress. To answer your question, since Carbon-14 has a half-life of approximately 5,730 years, we can use the formula N = N0 * (1/2)^(t/t1/2), where N is the remaining amount, N0 is the initial amount, t is the time elapsed, and t1/2 is the half-life.

In this case, if the mammoth's fossil sample has 1 gram left, we have N = 1 gram and N0 = 8 grams. Rearranging the formula, we get:

1 = 8 * (1/2)^(t/5730)

Let's solve this equation and find out how many half-lives have passed!

Well, look at that! It turns out there have been 3 half-lives, since 1/2^(3) = 1/8. So, in this fossil sample, three half-lives have passed.

As for the years that have gone by since the mammoth's death, we know that each half-life is approximately 5,730 years. Since 3 half-lives have passed, we can multiply 5,730 years by 3 to estimate that around 17,190 years have elapsed since the poor mammoth's untimely demise.

The moral of the story? Even mammoths can't escape the passage of time, but at least they leave us with some fossil humor to ponder.

## To determine the number of half-lives that have passed, we can use the half-life of Carbon-14, which is approximately 5730 years. We can calculate the number of half-lives by dividing the initial amount of Carbon-14 by the amount remaining.

1 gram (remaining) divided by 8 grams (initial amount) equals 0.125.

Now, we can calculate the number of half-lives using the formula:

number of half-lives = log(base 0.5) of (0.125)

Using a logarithm calculator, we find that the number of half-lives is approximately 3.3219.

Since we can't have a fraction of a half-life, we round down to the nearest whole number. Therefore, 3 half-lives have passed.

To calculate the number of years that have passed since the mammoth's death, we multiply the number of half-lives by the half-life of Carbon-14.

3 half-lives multiplied by 5730 years equals 17190 years.

Therefore, approximately 17190 years have passed since the mammoth's death.

## To determine how many half-lives have passed, we need to use the concept that the amount of Carbon-14 in a sample decreases by half after each half-life.

1. Start with the initial amount of Carbon-14 in the mammoth, which is 8 grams.
2. Divide the current amount of Carbon-14 in the fossil sample, which is 1 gram, by the initial amount of Carbon-14.
1 / 8 = 0.125
3. Take the logarithm (base 2) of this ratio to calculate the number of half-lives.
log₂(0.125) ≈ -3
Therefore, approximately 3 half-lives have passed.

To determine the number of years that have passed since the mammoth's death, we need to know the half-life of Carbon-14. The half-life of Carbon-14 is approximately 5730 years.

1. Multiply the number of half-lives by the half-life of Carbon-14.
3 x 5730 = 17190 years
Therefore, approximately 17190 years have passed since the mammoth's death.