Exploring Exponential Growth and Decay Concepts

The video tutorial covers exponential growth and decay, explaining how to write equations for these situations. It discusses the components of growth and decay functions, such as the initial amount, rate, and time. The tutorial provides examples, including car depreciation, investment growth, employee growth, and iPhone depreciation, demonstrating how to calculate values over time using exponential functions.

What variable in the exponential function represents the initial amount?

• b

• a

• x

• r

What does the variable 'x' typically represent in exponential growth and decay formulas?

• Time period

• Initial amount

• Rate of change

• Percentage increase

In an exponential growth equation, what does 'b' represent when the growth rate is 3%?

• 0.03

• 1.03

• 3

• 0.97

Why must the base 'b' be greater than one in a growth scenario?

• To ensure decay

• To ensure stability

• To ensure reduction

• To ensure increase

For a decay rate of 3%, what is the correct value of 'b' in the decay formula?

• 0.03

• 1.03

• 0.97

• 3

What does the formula 'y = a(1 - r)^x' calculate in a practical scenario?

• Time passed

• Decay over time

• Initial amount

• Growth over time

In the context of exponential functions, what does subtracting the rate from one calculate?

• Initial value

• Decay factor

• Future value

• Growth factor

How is the car's value calculated after 7 years if it depreciates by 10% annually?

• y = 50000(0.9)^7

• y = 50000(1.1)^7

• y = 50000(0.1)^7

• y = 50000(1 - 0.1)^7

What is the value of an investment after 18 years if it grows by 9% annually?

• y = 1800(1.09)^18

• y = 1800(0.91)^18

• y = 1800(0.09)^18

• y = 1800(1 - 0.09)^18

What is the final amount of an investment that starts at $1,800 and grows at 9% per year over 18 years?

• $7,500.00

• $9,000.00

• $8,000.00

• $8,490.82