Exponential Functions and Radioactive Decay

The video tutorial explains the concept of half-life using radium 226, which has a half-life of 1,590 years. It discusses two exponential decay functions, highlighting their differences and how to choose between them. The tutorial models the decay of radium 226 using an exponential function and calculates the remaining amount after 2,500 years, demonstrating the process with a calculator. The tutorial emphasizes that either function could be used to achieve the same result, though one may require more work.

What is the half-life of Radium 226?

• 1,590 years

• 2,500 years

• 1,000 years

• 3,000 years

Which of the following is NOT a component of the first exponential function discussed?

• Initial amount 'A'

• Decay rate 'R'

• Continuous decay rate 'K'

• Time 'T'

In the second exponential function, what does 'K' represent?

• Time

• Continuous decay rate

• Decay rate per unit time

• Initial amount

What is the main difference between the two exponential functions discussed?

• One is for growth, the other for decay

• One is simpler to use

• One is more accurate than the other

• One uses a continuous decay rate, the other does not

What is the purpose of dividing 'T' by 1,590 in the exponential function?

• To ensure the exponent equals one at half-life

• To adjust the decay rate

• To calculate the initial amount

• To convert time to seconds

How much of the 100 milligrams of Radium 226 remains after 2,500 years?

• 33.6 milligrams

• 10 milligrams

• 25 milligrams

• 50 milligrams

What is the initial amount 'A' used in the calculation?

• 200 milligrams

• 100 milligrams

• 150 milligrams

• 50 milligrams

What is the exponent used in the calculation for the remaining amount after 2,500 years?

• 2,500

• 1,590

• 1,590 divided by 2,500

• 2,500 divided by 1,590

What is the main advantage of using the first exponential function over the second?

• It is easier to understand

• It uses a continuous decay rate

• It requires less calculation

• It is more accurate

Why might the second function take more work to use?

• It requires more data

• It involves complex calculations

• It uses a continuous decay rate

• It is less accurate