Final answer:
Using the half-life of carbon-14, which is 5,730 years, and calculating based on the remaining 20% of carbon-14, the age of the fossil is determined to be approximately 11,460 years old.
Step-by-step explanation:
To determine the age of the fossil which contains 20% of its original carbon-14, we will use the half-life of carbon-14, which is 5,730 years. Since carbon-14 decreases by half every 5,730 years, we can use a simple mathematical calculation involving logarithms to solve for the time passed (the age of the fossil).
First, we express the remaining carbon-14 as a fraction (20% = 0.20), and then we use the half-life formula:
N = N0(1/2)^(t/t1/2)
where N is the remaining amount of carbon-14, N0 is the original amount, t is the age of the fossil, and t1/2 is the half-life of carbon-14.
Substituting the values, we get:
0.20 = (1/2)^(t/5730)
By taking the logarithm of both sides and rearranging the equation, we arrive at:
t = 5730 * log(0.20) / log(0.5)
After solving, we find that the fossil is approximately 11,460 years old.