Exploring Exponential and Linear Functions

The video tutorial explains the differences between linear and exponential functions. Linear functions grow or decrease at a constant rate by adding or subtracting the same number, while exponential functions grow or decay at a constant growth or decay factor by multiplying. The tutorial provides methods to identify these functions using tables and offers real-world examples, such as earning a fixed amount daily (linear) versus receiving a percentage raise annually (exponential). Key terms and concepts are highlighted to aid in solving word problems.

What is the key characteristic of a linear function?

• It grows by a constant percentage.

• It grows by adding or subtracting the same number.

• It grows by multiplying by the same number.

• It grows by a variable rate.

How does an exponential function grow or decay?

• By multiplying by a constant factor.

• By subtracting a constant number.

• By dividing by a constant factor.

• By adding a constant number.

In a table of values, what indicates that a function is linear?

• The x-values increase by a variable amount.

• The x-values increase by a constant factor.

• The y-values increase by a constant amount.

• The y-values increase by a constant factor.

If the y-values in a table increase by 3 each time the x-values increase by 1, what type of function is it?

• Neither

• Linear

• Exponential

• Quadratic

What should you check first when determining if a function is linear or exponential?

• The growth factor of x-values.

• The constant rate of y-values.

• The constant rate of x-values.

• The growth factor of y-values.

If the y-values in a table are multiplied by 3 each time the x-values increase by 1, what type of function is it?

• Linear

• Exponential

• Neither

• Quadratic

What does it mean if a table of values does not show a constant rate of change or a constant growth factor?

• The function is linear.

• The function is exponential.

• The function is neither linear nor exponential.

• The function is quadratic.

If a table of values shows y-values increasing by 5, then 30, what type of function is it?

• Neither

• Exponential

• Linear

• Quadratic

If you earn $10 every day, what type of growth is this?

• Quadratic

• Neither

• Linear

• Exponential

If you receive a 20% raise every year, what type of growth is this?

• Linear

• Exponential

• Neither

• Quadratic