Question

An artifact originally had 16 grams of carbon-14 present. The decay model A=16e −0.000121t describes the amount of carbon-14 present after t years. Use the model to determine how many grams of carbon-14 will be present in 5941 years. The amount of carbon-14 present in 5941 years will be approximately grams.

Answer 1

The amount of carbon-14 present in 5941 years will be approximately 4.7 grams.

Step-by-step explanation:

The decay model A=16e-0.000121t describes the amount of carbon-14 present after t years. To determine how many grams of carbon-14 will be present in 5941 years, we can substitute t = 5941 into the equation.

A = 16e-0.000121(5941)

Calculating this equation, we find that the amount of carbon-14 present in 5941 years will be approximately 4.7 grams.

Answer 2

Using the half-life of carbon-14 and the decay formula, we can calculate the amount of carbon-14 an artifact originally contained from the current observed amount after a given number of years.

Step-by-step explanation:

To determine how much carbon-14 an artifact originally contained, we use the concept of radiometric dating, particularly focusing on carbon dating. Given the artifact contains 8.4 × 10^-9 grams of carbon-14 after 10,670 years, and knowing that the half-life of carbon-14 is 5,730 years, we can use the decay formula:

A = A0e^−0.693t/T1/2

Where A is the current amount of carbon-14, A0 is the original amount, t is the time that has passed, and T1/2 is the half-life of carbon-14. Using this formula, we can solve for A0 knowing that A is 8.4 × 10^-9 grams and t is 10,670 years, to find the original amount of carbon-14.