Carbon-14 Decay and Half-Life Concepts

The video tutorial explains how carbon-14, an element, loses half of its mass every 5730 years. It guides viewers through modeling the decay of carbon-14 using a function that depends on time in years. The tutorial starts with a table to understand the decay process and then develops a function to calculate the remaining mass over time. The function is generalized to account for any number of half-lives, and the tutorial concludes with a finalized model that accurately represents the decay process.

What is the half-life of Carbon-14?

• 6000 years

• 5000 years

• 7000 years

• 5730 years

What is the initial mass of the Carbon-14 sample used in the example?

• 741 grams

• 500 grams

• 1000 grams

• 600 grams

If the initial mass of a Carbon-14 sample is 741 grams, what is the mass after one half-life?

• 370.5 grams

• 300 grams

• 350 grams

• 400 grams

How many times do you multiply by one-half after two half-lives?

• Four times

• Three times

• Once

• Twice

What happens to the mass of Carbon-14 after three half-lives?

• It remains the same

• It is reduced to one-half of the original mass

• It is reduced to one-fourth of the original mass

• It is reduced to one-eighth of the original mass

What is the mass of Carbon-14 after two half-lives if the initial mass is 741 grams?

• 185.25 grams

• 370.5 grams

• 92.625 grams

• 741 grams

What is the general form of the function that models the mass of Carbon-14 over time?

• m(t) = 741 * (1/2)^t

• m(t) = 741 * 2^(t/5730)

• m(t) = 741 * (1/2)^(t/5730)

• m(t) = 741 * t/5730

What type of function is used to model the decay of Carbon-14?

• Quadratic function

• Logarithmic function

• Exponential function

• Linear function

How do you determine the number of half-lives that have passed?

• By dividing t by 5730

• By subtracting 5730 from t

• By adding 5730 to t

• By multiplying t by 5730

What is the purpose of dividing t by the half-life in the function?

• To adjust the mass to zero

• To find the total time elapsed

• To calculate the initial mass

• To determine the number of half-lives that have passed