Understanding Exponential Decay Concepts

This video tutorial explains exponential decay, a process where a quantity decreases by a percentage over time. It introduces the formula y = a * (1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time. Two examples are provided: car depreciation and stock value decline, illustrating how to apply the formula to calculate the remaining value over time. The video concludes with a summary of key points about exponential decay.

What is exponential decay?

• A decrease in quantity at a percentage each period

• A decrease in quantity at a constant rate

• An increase in quantity at a percentage each period

• An increase in quantity over time

Which formula represents exponential decay?

• y = a * (1 - r)^t

• y = a * (1 + r)^t

• y = a * r^t

• y = a * t^r

In the car depreciation example, what is the initial value of the car?

• $25,000

• $20,000

• $23,000

• $30,000

What is the rate of depreciation for the car each year?

• 20%

• 15%

• 12%

• 10%

How do you calculate the car's value after a certain number of years?

• Subtract the rate of depreciation from the initial value

• Multiply the initial value by the rate of depreciation

• Use the formula y = a * (1 - r)^t

• Add the rate of depreciation to the initial value

What is the car's value after 4 years?

• $12,600

• $10,000

• $18,000

• $15,000

What does buying shares of stock represent?

• Owning a part of a company

• Buying a product from a company

• Selling a part of a company

• Lending money to a company

What happened to the stock value in the example?

• It decreased by 2% each year

• It increased by 5% each year

• It remained constant

• It increased by 2% each year

What is the initial value of the stock in the example?

• $500

• $400

• $700

• $600

What is the rate of depreciation for the stock each year?

• 1%

• 2%

• 4%

• 3%