Exponential Functions and Their Properties

This video tutorial covers exponential growth and decay functions, focusing on rewriting equations into exponential form to identify the percent rate of increase or decrease. It explains the components of exponential functions, including the initial amount, rate of change, and time. The tutorial provides examples of rewriting exponential decay and growth functions, demonstrating how to calculate and interpret growth and decay factors.

What is the main focus of the video tutorial?

• Exponential growth and decay functions

• Quadratic functions

• Trigonometric identities

• Linear equations

What does the variable 'a' represent in the exponential function?

• The rate of increase

• The initial amount

• The ending amount

• The time period

How is the percent rate of increase or decrease represented in the function?

• As a percentage

• As a decimal

• As a whole number

• As a fraction

What does the '1' in the expression '1 + r' or '1 - r' signify?

• The original amount

• The decay factor

• The growth factor

• The time period

In the context of exponential functions, what is a growth factor?

• A factor less than 1

• A factor equal to 1

• A factor greater than 1

• A factor equal to 0

What is the decay factor in an exponential function?

• 1

• 1 - r

• 1 + r

• r

In Example 1, what is the base of the rewritten exponential decay function?

• 0.68

• 1.45

• 0.32

• 0.75

What is the rate of decay in Example 1 after converting to a percentage?

• 33%

• 32%

• 45%

• 68%

In Example 2, what is the initial amount in the rewritten function?

• 100

• 33

• 0.33

• 50

What is the rate of increase in Example 2 after converting to a percentage?

• 68%

• 32%

• 33%

• 45%