Exponential Functions and Rates

This video tutorial explains exponential functions in two forms: F(x) = A * B^x and F(x) = A * e^(Kx). It covers how to determine growth and decay rates, both per unit of time and continuously. The tutorial includes examples of calculating growth rates for cell phone usage and depreciation rates for a computer, demonstrating how to convert between the two forms of exponential functions.

What is the initial or starting amount in the exponential function F(x) = A * B^x?

• B

• x

• R

• A

If the base B in the function F(x) = A * B^x is greater than 1, what does it indicate?

• No change

• Constant rate

• Exponential growth

• Exponential decay

In the function F(x) = A * e^(Kx), what does a positive K indicate?

• No change

• Exponential growth

• Exponential decay

• Constant rate

How do you determine the annual growth rate from the base B in the function F(x) = A * B^x?

• R = B - 1

• R = B + 1

• R = 1 - B

• R = B * 1

What is the continuous growth rate if the base B is 1.33?

• 14.3%

• 11.49%

• 13.3%

• 12.49%

In the cell phone example, what is the annual growth rate if B is 1.33?

• 13.3%

• 11.49%

• 14.3%

• 12.49%

What is the continuous depreciation rate if K is -0.325?

• 32.5%

• 27.75%

• 30.5%

• 25.5%

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

• R = B - 1

• R = B * 1

• R = 1 - B

• R = B + 1

In the computer depreciation example, what is the annual depreciation rate if B is approximately 0.7225?

• 25.5%

• 32.5%

• 30.5%

• 27.75%

What is the equivalent exponential function form for V(T) = 1500 * e^(-0.325T)?

• V(T) = 1500 * 0.85^T

• V(T) = 1500 * 1.33^T

• V(T) = 1500 * 0.7225^T

• V(T) = 1500 * 1.25^T