Question

a hiker in africa discovers a skull that contains 32% of its original amount of c 14 find the age of the skull to the nearest year

Answer 1

The half-life of carbon-14 is 5,730 years. This means that every 5,730 years, half of the carbon-14 in a sample will decay. So, if a sample contains 32% of its original amount of carbon-14, it is about 2 * 5,730 = 11,460 years old.

However, it is essential to note that radiocarbon dating is not an exact science. There is a margin of error of about 20 years. So, the skull's actual age could be between 11,260 and 11,660 years old.

Here is a formula that can be used to calculate the age of a sample using radiocarbon dating:

```

Age = (5,730 * ln(A/Ao)) / ln(2)

```

Where:

* Age is the age of the sample in years

* A is the amount of carbon-14 in the sample

* Ao is the original amount of carbon-14 in the sample

* ln is the natural logarithm function

In this case, A = 0.32 and Ao = 1.0. So, the age of the skull is:

```

Age = (5,730 * ln(0.32) / ln(2)) = 11,460 years

```

Explanation:

Answer 2

4535 years.

Explanation:

The formula used to calculate the age of a sample by carbon-14 dating is3:

t=−0.693ln(N0​Nf​​)​×t1/2​

where:

t is the age of the sample

Nf is the number of carbon-14 atoms in the sample after time t

N0 is the number of carbon-14 atoms in the original sample

t1/2 is the half-life of carbon-14 (5730 years)

In your case, the skull contains 32% of its original amount of carbon-14, which means that Nf/N0 = 0.32. You can plug in this value and the half-life into the formula and get:

t=−0.693ln(10.32​)​×5730

Using a calculator, you can simplify this expression and get:

t=−1.139×−0.693×5730

t=4534.7