Carbon-14 Decay and Half-Life Concepts

The video tutorial explains how to determine the age of a wooden artifact using carbon-14 dating. It covers the concept of half-life, the calculation of the exponential decay rate, and the application of these concepts to solve for the time elapsed since the artifact was made. The tutorial concludes with a calculation showing the artifact is approximately 4,223 years old.

What percentage of carbon-14 is present in the wooden artifact compared to living trees?

• 70%

• 40%

• 50%

• 60%

What is the half-life of carbon-14?

• 5,730 years

• 5,000 years

• 6,000 years

• 6,500 years

What does the variable K represent in the exponential decay function?

• Final amount

• Decay rate constant

• Time

• Initial amount

How is the decay rate constant (K) calculated using the half-life of carbon-14?

• By multiplying the half-life by the natural log of 2

• By dividing the natural log of 0.5 by the half-life

• By adding the half-life to the natural log of 2

• By subtracting the natural log of 0.5 from the half-life

What is the value of the decay rate constant (K) for carbon-14?

• 0.000000012968

• 0.000012968

• 0.0000012968

• 0.00000012968

What is the exponential decay model used to determine the age of the artifact?

• P(t) = P0 * e^(K / t)

• P(t) = P0 * e^(K * t)

• P(t) = P0 * e^(-K * t)

• P(t) = P0 * e^(t / K)

If 60% of carbon-14 is present, what is the value of P(t) in the decay model?

• 0.7

• 0.6

• 0.5

• 0.4

What mathematical operation is used to solve for time (t) in the decay model?

• Division

• Multiplication

• Subtraction

• Addition

How old is the artifact, according to the final calculation?

• 5,223 years

• 4,223 years

• 3,223 years

• 6,223 years

What is the purpose of taking the natural log of both sides in the decay equation?

• To simplify the equation

• To eliminate the exponential

• To find the initial amount

• To determine the final amount