Understanding Half-Life and Exponential Decay

The video tutorial explains how to calculate the initial mass and remaining mass of a palladium-100 sample using its half-life and exponential decay formula. It covers determining the decay rate, solving for the initial mass, and calculating the mass after a specified period using logarithms and exponential functions.

What is the half-life of platinum 100 as mentioned in the video?

• 6 days

• 4 days

• 2 days

• 8 days

Which variable in the exponential function represents the initial amount?

• t

• k

• p₀

• p(t)

How is the decay constant (k) determined using the half-life?

• By dividing the half-life by the initial mass

• By multiplying the half-life by the initial mass

• By taking the natural log of the half-life

• By using the natural log of one-half divided by the half-life

What is the significance of the natural log in the exponential decay formula?

• It represents the initial mass

• It helps in calculating the decay constant

• It determines the time period

• It is used to find the final mass

What is the initial mass of the palladium 100 sample after 12 days?

• 12 milligrams

• 48 milligrams

• 6 milligrams

• 24 milligrams

What is the value of the exponent when calculating the initial mass after 12 days?

• 2

• 3

• 4

• 1

Which mathematical operation is used to solve for the initial mass in the exponential function?

• Multiplication

• Addition

• Subtraction

• Division

How many days are equivalent to 7 weeks?

• 56 days

• 49 days

• 42 days

• 35 days

What is the approximate mass of palladium 100 left after 7 weeks?

• 0.1999 milligrams

• 0.0999 milligrams

• 0.0199 milligrams

• 0.0099 milligrams

What is the equivalent decimal value of 1/4 used in the calculations?

• 0.30

• 0.25

• 0.20

• 0.15