Linear or Exponential?

​Is it Linear or Exponential?

​Before you begin this practice... you will want to have out the notes from Friday.

They are titled, "Linear vs. Exponential"

​If you were absent, the next four slides should help guide you through this practice.

When in doubt, please refer back to the first four slides for help.

​Is it Linear or Exponential?

​When given a table, look for a common difference or a common ratio.

​- If the pattern is add/subtract, the function is linear.

​- If the pattern is multiply/divide, the function is exponential.

​Examples:

Since the pattern is adding, the function is linear.

Since the pattern is multiplying, the function is exponential.

​Finding the Common Ratio

​To find the common ratio or "b" value, simply divide the last number by the previous number

​For Example:

​Therefore, the common ratio or"b" value is 2.

The multiplier is 2!

​Finding the "a" value or y-intercept

​To find the y-intercept, just look for the x-value of zero and the corresponding y-value is the y-intercept.

Examples:

The y-intercept here is 8

The y-intercept here is 2

​Writing the "rule" or equation

​Once we now what the "a" and "b" values are, we can write the equation that represents the function.

​For Example:

​We found earlier that

a = 8

b = 2

​- We use the template: y = a(b)^x

​y = 8(2)^x

Multiple Choice

Is the equation linear or exponential?

• Linear Equation

• Exponential Equation

Multiple Choice

Is the equation linear or exponential?

• Linear Equation

• Exponential Equation

Multiple Choice

Is the equation linear or exponential?

• Linear Equation

• Exponential Equation

Multiple Choice

Is the equation linear or exponential?

• Linear Equation

• Exponential Equation

Multiple Choice

Is the equation linear or exponential?

• Linear Equation

• Exponential Equation

Multiple Choice

Is the graph linear or exponential?

• Linear Graph

• Exponential Graph

Multiple Choice

Is the graph linear or exponential?

• Linear Graph

• Exponential Graph

Multiple Choice

Is the graph linear or exponential?

• Linear Graph

• Exponential Graph

Multiple Choice

Is the graph linear or exponential?

• Linear Graph

• Exponential Graph

Multiple Choice

Is the graph linear or exponential?

• Linear Graph

• Exponential Graph

Multiple Choice

Is the table linear or exponential?

• Linear Table

• Exponential Table

Multiple Choice

Is the table linear or exponential?

• Linear Table

• Exponential Table

Multiple Choice

Is the table linear or exponential?

• Linear Table

• Exponential Table

Multiple Choice

Is the table linear or exponential?

• Linear Table

• Exponential Table

Multiple Choice

Is the table linear or exponential?

• Linear Table

• Exponential Table

Multiple Choice

Is the table linear or exponential?

• Linear Table

• Exponential Table

Multiple Choice

Is the situation linear or exponential?

• Linear Situation

• Exponential Situation

Multiple Choice

Is the situation linear or exponential?

• Linear Situation

• Exponential Situation

Multiple Choice

Is the situation linear or exponential?

• Linear Situation

• Exponential Situation

Multiple Choice

Is the situation linear or exponential?

• Linear Situation

• Exponential Situation

Multiple Choice

Linear or Exponential?

A virus infected double the population every day.

• Linear

• Exponential

Multiple Choice

Linear or Exponential?

Maria's capacity to learn a lesson triples every week.

• Linear

• Exponential

Multiple Choice

Linear or Exponential?

• Linear

• Exponential

Multiple Choice

Linear or Exponential?

• Linear

• Exponential

Multiple Choice

Linear or Exponential?

1, 4, 16, 64, ...

• Linear

• Exponential

Multiple Choice

Linear or Exponential?

4, 8, 12, 16, ...

• Linear

• Exponential

Multiple Choice

Linear or Exponential?

$$40,\ 20,\ 10,\ 5,\ ...$$  

• Linear

• Exponential

Multiple Choice

Is the pattern adding/subtracting or multiplying/dividing?

• adding/subtracting

• multiplying/dividing

Multiple Choice

Is the function linear or exponential?

• linear

• exponential

Multiple Choice

What is the common ratio or "b" value?

• 3

• 1/3

• 9

• 2

Match

Match each table with the correct "a" value.

3

5

2

1/3

• 3

• 5

• 2

• 1/3

Multiple Choice

What is the y-intercept or "a" value?

• 1/3

• 1

• 3

• 9

Multiple Choice

What is the equation that models the data in the table?

Use the formula: y=a(b)^x

• y = 3(3)^x

• $$y=\frac{1}{3}\left(3\right)^x$$  

• $$y=\left(\frac{1}{3}\right)^x$$  

• y = 3^x

Multiple Choice

Is the pattern adding/subtracting or multiplying/dividing?

• adding/subtracting

• multiplying/dividing

Multiple Choice

Is the function linear or exponential?

• linear

• exponential

Multiple Choice

What is the common ratio or "b" value?

• 1/2

• 2

• 4

• 8

Multiple Choice

What is the y-intercept or "a" value?

• 1/2

• 2

• 4

• 8

Multiple Choice

What is the equation that models the data in the table?

• $$y=2^x$$  

• $$y=2\left(2\right)^x$$  

• $$y=4\left(2\right)^x$$  

• $$y=2\left(4\right)^x$$  

Multiple Choice

What type of function is pictured?

• Linear

• Exponential

• Neither

Multiple Choice

Is the graph illustrating a linear function, exponential function, or neither?

• Linear

• Exponential

• Neither