Exponential Functions and Depreciation Rates

The video tutorial explains how to determine the value of a car over time using an exponential function. It covers the calculation of continuous and annual depreciation rates, highlighting the differences between them. The tutorial also demonstrates how to verify the equivalence of two exponential functions using a graphing calculator.

What is the initial value of the car according to the given function?

• $21,000

• $25,000

• $30,000

• $15,000

What does a negative K value in the exponential function indicate?

• Exponential growth

• Exponential decay

• Constant value

• Linear growth

How is the continuous depreciation rate determined from the function?

• By multiplying the initial value by K

• By taking the absolute value of K

• By adding K to the initial value

• By dividing the initial value by K

What is the continuous depreciation rate of the car?

• 12.5%

• 18.5%

• 10.5%

• 15.5%

How do you calculate the base B for the annual depreciation rate?

• B = e^K

• B = K - 1

• B = K^e

• B = 1 + K

What is the equivalent annual depreciation rate derived from the function?

• 14.36%

• 13.36%

• 12.36%

• 15.36%

What is the rewritten form of the exponential function?

• F(t) = 21,000 * 0.8564^T

• F(t) = 21,000 * 0.9564^T

• F(t) = 21,000 * 1.0564^T

• F(t) = 21,000 * 1.1564^T

Why might there be a slight difference between the two functions when graphed?

• Due to incorrect calculator settings

• Due to rounding of the initial value

• Due to incorrect function form

• Due to rounding of the base B

What feature of the graphing calculator is used to compare the two functions?

• Trace feature

• Zoom feature

• Table feature

• Graph feature

What conclusion can be drawn from the graph comparison of the two functions?

• The functions are approximately equivalent

• The functions have different initial values

• The functions are not equivalent

• The functions are exactly the same