Understanding Exponential Decay

The video tutorial explains the concept of half-life using cesium-137 as an example. It covers exponential decay functions, reviews exponential notation, and addresses common misunderstandings. The tutorial compares exponential growth and decay, illustrating the process with function tables and graphs. It concludes by predicting when cesium-137 will decay below 100 kilograms, emphasizing that while decay is rapid initially, the substance never fully disappears.

What is the half-life of cesium-137?

• 90 years

• 60 years

• 30 years

• 15 years

In exponential notation, what does the exponent indicate?

• The number of times the base is added

• The number of times the base is divided

• The number of times the base is used as a factor

• The number of times the base is subtracted

What is a common misunderstanding when raising a fraction to a power?

• Not applying the power at all

• Applying the power to both numerator and denominator

• Applying the power to the denominator only

• Applying the power to the numerator only

What happens to a quantity during exponential growth?

• It increases

• It fluctuates

• It remains constant

• It decreases

After two half-lives, what fraction of the original amount remains?

• 1/2

• 1/4

• 1/8

• 1/16

How many kilograms of cesium-137 remain after 150 years?

• 200 kilograms

• 150 kilograms

• 100 kilograms

• 93 kilograms

What does the graph of an exponential decay function do over time?

• Crosses the x-axis

• Levels off and never crosses the x-axis

• Increases indefinitely

• Decreases to zero