Exponential Functions and Their Properties

The video tutorial covers exponential growth and decay, explaining the structure of exponential functions, growth and decay factors, and their differences from linear functions. It provides examples and guides on creating exponential equations, introduces doubling and half-life formulas, and demonstrates graphing techniques for exponential functions.

What is the key characteristic of an exponential function?

• The variable is in the exponent.

• The variable is in the base.

• The function is always linear.

• The function has no exponent.

What must the initial value in an exponential function not be?

• Less than zero

• Greater than zero

• Equal to zero

• A negative number

How does a linear function differ from an exponential function?

• Exponential functions add a constant amount.

• Linear functions add a constant amount.

• Linear functions multiply by a constant factor.

• Exponential functions have no constant factor.

What is the condition for a function to be considered exponential?

• The base must be a constant.

• The exponent must be a constant.

• The exponent must be a variable.

• The base must be a variable.

In an exponential equation, what does the growth factor represent?

• The variable term

• The constant term

• The rate of increase or decrease

• The initial value

What does the half-life formula help determine?

• The growth factor of a quantity

• The initial value of a quantity

• The time it takes for a quantity to halve

• The time it takes for a quantity to double

What is an asymptote in the context of graphing exponential functions?

• A point where the graph ends

• A point where the graph starts

• A line that the graph approaches but never touches

• A line that the graph crosses