Using half life to determine the age of a piece of coal

The video tutorial covers compound interest formulas, focusing on continuous compounding and the carbon-14 half-life concept. It explains how to determine the rate of decay and solve for time using logarithms, with a practical example involving ancient coal. The tutorial concludes with a detailed calculation to find the age of the coal based on its carbon content.

What does the variable 'A' represent in the compound interest formula y = a * E^(RT)?

• The initial value

• The rate of interest

• The final value

• The time period

What is the half-life of Carbon-14?

• 5000 years

• 5730 years

• 6000 years

• 7000 years

If the initial amount of a substance is 100 grams, how much will remain after one half-life?

• 100 grams

• 25 grams

• 50 grams

• 75 grams

Which mathematical operation is used to isolate the variable R in the decay formula?

• Subtraction

• Addition

• Logarithm

• Multiplication

What is the formula used to calculate the rate of decay R?

• R = Ln(1/2) / T

• R = Ln(2) / T

• R = 2 * T

• R = 1/2 * T

If an ancient piece of coal has 15% of the carbon compared to a modern piece, how old is the coal?

• 12,000 years

• 15,682 years

• 20,000 years

• 10,000 years

What is the significance of the natural logarithm (Ln) in solving for the age of the coal?

• It isolates the variable T

• It provides an exact integer value

• It converts the equation to exponential form

• It helps in approximating the age