Half-Life Calculations and Logarithms

The video tutorial explains how to solve a half-life problem involving a radioactive substance. Starting with 60 pounds, the substance reduces to 48 pounds over three years. The tutorial walks through the process of setting up the equation, understanding the variables, and using logarithms to solve for the half-life, which is calculated to be approximately 9.3 years.

What was the initial amount of the radioactive substance left in the garage?

• 3 pounds

• 9.3 pounds

• 60 pounds

• 48 pounds

After how many years was the remaining amount of the substance measured?

• 3 years

• 2 years

• 4 years

• 1 year

What is the remaining amount of the substance after three years?

• 60 pounds

• 30 pounds

• 24 pounds

• 48 pounds

What is the first step in solving the half-life equation?

• Add 60 to both sides

• Divide both sides by 60

• Subtract 60 from both sides

• Multiply both sides by 60

What mathematical operation is used to bring down the exponent in the equation?

• Multiplication

• Subtraction

• Addition

• Logarithm

What is the purpose of using logarithms in the half-life calculation?

• To add the exponents

• To divide the exponents

• To multiply the exponents

• To bring down the exponent

Which property of logarithms is used to solve for the half-life?

• Logarithm of a product

• Logarithm of a sum

• Logarithm of a quotient

• Logarithm of a power

What is the approximate half-life of the radioactive substance?

• 12 years

• 9.3 years

• 6.5 years

• 3 years

What is the final step to isolate the half-life variable in the equation?

• Subtract log 0.8 from both sides

• Multiply both sides by log 0.8

• Divide both sides by log 0.8

• Add log 0.8 to both sides