Question

Carbon-14 is a radioactive isotope of carbon that is used to date fossils. There are about 1.5

atoms of cafbon-14 for every trillion atoms of carbon in the atmosphere, known as 1.5 ppt
(parts per trillion). Carbon in a living organism has the same concentration as carbon-14. When
an organism dies, the carbon-14 content decays at a rate of 11.4% per millennium (1000 years).
Write an equation for carbon-14 concentration (in ppt) as a function of time (in millennia) and
determine how old a fossil must be that has a measured concentration of 0.3 ppt.

Answer 1

In carbon dating, the Carbon-14 concentration decays exponentially, and can be described by a formula involving its initial concentration and decay rate. To find a fossil's age with a concentration of 0.3 ppt, we use this decay formula, solve for t (time in millennia), and calculate the fossil's age.

Step-by-step explanation:

To determine the Carbon-14 concentration as a function of time and the age of a fossil with a concentration of 0.3 ppt, we will use the formula of exponential decay based on the half-life concept in carbon dating.

The formula for the carbon-14 concentration as a function of time (t, in millennia) is:

C(t) = C_0 × (1 - 0.114)^t

Where:

• C(t) is the Carbon-14 concentration at time t,
• C_0 is the initial Carbon-14 concentration (1.5 ppt), and
• 0.114 is the rate of decay per millennium (11.4%).

To find the age of a fossil with a measured concentration of 0.3 ppt, we solve for t in the above equation with C(t) set to 0.3 ppt:

0.3 = 1.5 × (1 - 0.114)^t

Dividing both sides by 1.5 and taking the natural logarithm:

t = ln(0.3/1.5) / ln(1 - 0.114)

Solving this gives us the age of the fossil in millennia.

Answer 2

Function: A=1.5(1+0.114)^1000

Step-by-step explanation:

1.5 is the initial amount and 0.114 in the rate and the 1000 is the time