Understanding Exponential Decay in Real-Life Scenarios

The video tutorial discusses two scenarios involving exponential decay: the cooling of coffee and the population decline of a town after a mill closure. It evaluates different graph models to determine which best represents the exponential decrease in temperature and population, emphasizing the approach towards a stable state, such as room temperature or a lower population limit.

What is the initial temperature of the coffee when it is poured?

• 90 degrees Celsius

• 80 degrees Celsius

• 70 degrees Celsius

• 100 degrees Celsius

Which temperature does the coffee approach as time increases?

• 40 degrees Celsius

• 30 degrees Celsius

• 20 degrees Celsius

• 10 degrees Celsius

What type of graph best represents the cooling of the coffee?

• Linear

• Quadratic

• Exponential

• Logarithmic

Why is graph B ruled out as a model for the coffee cooling?

• It starts at the wrong temperature

• It approaches zero degrees

• It is a quadratic model

• It is a logarithmic model

What is the main issue with graph C in representing the coffee cooling?

• It starts at a lower temperature

• It linearly decreases then stops

• It is a quadratic model

• It approaches a higher temperature

What is the initial population of the town after the mills close?

• 30,000

• 50,000

• 40,000

• 20,000

What does the population of the town approach over time?

• 20,000

• 15,000

• 25,000

• 10,000

What type of decay does the town's population experience?

• Linear

• Exponential

• Quadratic

• Logarithmic

How many years does it take for the population to fall below 22,000?

• 20 years

• 10 years

• 25 years

• 15 years

Which of the following is true about the population graph?

• It remains constant

• It approaches 20,000

• It increases over time

• It starts at 50,000