Linear vs Exponential Part 1

​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.

Multiple Choice

Is the pattern adding/subtracting or multiplying/dividing?

• adding/subtracting

• multiplying/dividing

Multiple Choice

Is the function linear or exponential?

• linear

• 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

​Use Desmos if you need to!

Multiple Choice

What is the common ratio or "b" value?

(Use Desmos if you need to!)

Divide 27/9 and 9/3.

• 3

• 1/3

• 9

• 2

Multiple Choice

What is the common ratio or "b" value?

(Use Desmos if you need to!)

Divide 32/16 and 16/8

• $$\frac{1}{2}$$

• 2

• 3

• 4

Multiple Choice

What is the common ratio or "b" value?

(Use Desmos if you need to!)

Divide 5/10 and 10/20

• $$\frac{1}{2}$$

• 2

• 5

• 10

​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

- This also means that the "a" value is 8.

- This also means that the "a" value is 2.

Match

Match each table with the correct "a" value.

3

5

2

1/3

• 3

• 5

• 2

• 1/3

Multiple Choice

Is the pattern adding/subtracting or multipying/dividing?

• adding/subtracting

• multipying/dividing

Multiple Choice

Is the linear or exponential?

• linear

• exponential

Multiple Choice

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

• 1/3

• 1

• 3

• 9

Multiple Choice

Is the function linear or exponential?

• linear

• exponential

Multiple Choice

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

• 1/2

• 2

• 4

• 8

Multiple Choice

What is the common ratio or "b" value?

(Use Desmos if you need to!)

• 1/2

• 2

• 4

• 8