Using Carbon dating to determine the age of a fossil

The video tutorial explains the concept of carbon dating and its use in determining the age of fossils. It introduces a mathematical model involving the ratio of carbon-14 to carbon-12 and demonstrates how to solve for the age of a fossil using logarithmic functions. The tutorial walks through the process of setting up the problem, solving the equation, and performing the final calculation to estimate the fossil's age, emphasizing the importance of understanding exponential and logarithmic properties.

What is the primary purpose of carbon dating?

• To calculate the weight of carbon in the atmosphere

• To determine the age of fossils

• To find the density of carbon in rocks

• To measure the amount of carbon in living organisms

Which two isotopes are compared in the carbon dating model?

• Carbon-14 and Carbon-15

• Carbon-12 and Carbon-14

• Carbon-13 and Carbon-14

• Carbon-12 and Carbon-13

What is the formula used in carbon dating to estimate the age of a fossil?

• r = 1 / 10^3 * E^(-T / 8267)

• r = 1 / 10^12 * E^(T / 8267)

• r = 1 / 10^3 * E^(T / 8267)

• r = 1 / 10^12 * E^(-T / 8267)

What is the first step in solving the carbon dating equation to find the age of a fossil?

• Multiply both sides by 10^12

• Subtract 10^12 from both sides

• Divide both sides by 10^12

• Add 10^12 to both sides

What mathematical operation is used to isolate the exponential function in the carbon dating equation?

• Multiplication

• Subtraction

• Division

• Addition

Which logarithmic property is used to solve the carbon dating equation?

• Log base 10 of 10 equals 1

• Log base e of e equals 1

• Log base 5 of 5 equals 1

• Log base 2 of 2 equals 1

What is the final step in calculating the age of a fossil using the carbon dating formula?

• Subtract the natural logarithm of 1/10

• Divide by the natural logarithm of 1/10

• Multiply by the natural logarithm of 1/10

• Add the natural logarithm of 1/10

What is the estimated age of the fossil calculated in the example?

• 19,035 years

• 19,000 years

• 19,103 years

• 19,350 years

Why is it important to use parentheses when calculating the natural logarithm in the carbon dating formula?

• To simplify the equation

• To ensure the correct order of operations

• To make the calculation faster

• To avoid syntax errors

What is the base of the natural logarithm used in the carbon dating calculation?

• Base 5

• Base e

• Base 2

• Base 10