Writing Exponenital Functions

​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!

​b = 2

Multiple Choice

What is the common ratio or "b" value?

(Use Desmos if you need to!)

• 2

• 3

• 6

• 1/2

​Finding the Common Ratio

​You could follow the same steps when finding the "b" value given a set of coordinates:

​For Example:

​Therefore, the common ratio or"b" value is 4

​b = 4

​An exponential in the form f(x) = bx includes the points (2,16), (3, 64) and (4, 256). What is the value of "b"?

​We only use the "y" values.

Math Response

An exponential function contains the points (2, 6), (3, 12) and (4, 24). What is the value of "b"?

(Use Desmos if you need to!)

Only write the number.

Type answer here

Correct Answer: 2

Deg^°

Rad

Math Response

An exponential function contains the points (-2, 81), (-1, 27) and (0, 9). What is the value of "b"?

(Use Desmos if you need to!)

Only write the number.

Type answer here

Correct Answer: \frac{1}{3}

Deg^°

Rad

​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 that:

a = 8

b = 2

​- We use the template: y = a(b)^x

​y = 8(2)^x

Multiple Choice

What is the common ratio or "a" value?

• 1/3

• 1

• 3

• 9

Multiple Choice

What is the common ratio or "b" value?

(Use Desmos if you need to!)

• 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

We found:

a = 1/3

b = 3

• y = 3(3)^x

• $$y=\frac{1}{3}\left(3\right)^x$$  

• $$y=\left(\frac{1}{3}\right)^x$$  

• y = 3^x

Multiple Choice

What is the "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

Multiple Choice

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

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

We found:

a = 2

b = 4

• $$y=2^x$$  

• $$y=2\left(2\right)^x$$  

• $$y=4\left(2\right)^x$$  

• $$y=2\left(4\right)^x$$  

Match

Match the correct exponential function with the given "a" and "b" values.

• a = 1

  b = 3

• a = 3

  b = ½

• a = 1

  b = ½

• a = ½

  b = 3

• a = 1

  b = 5

• $$y=3^x$$

• $$y=3\left(\frac{1}{2}\right)^x$$

• $$y=\left(\frac{1}{2}\right)^x$$

• $$y=\frac{1}{2}\left(3\right)^x$$

• $$y=5^x$$

Multiple Choice

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

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

• $$y=\left(\frac{1}{3}\right)^x$$  

• $$y=3^x$$  

• $$y=3\left(3\right)^x$$  

• $$y=\frac{1}{3}\left(3\right)^x$$  

Multiple Choice

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

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

• $$y=\frac{1}{2}\left(64\right)^x$$  

• $$y=128\left(\frac{1}{2}\right)^x$$  

• $$y=64\left(\frac{1}{2}\right)^x$$  

• $$y=\frac{1}{2}\left(128\right)^x$$  

Multiple Choice

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

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

• $$y=\frac{1}{2}\left(20\right)^x$$  

• $$y=20\left(\frac{1}{2}\right)^x$$  

• $$y=10\left(\frac{1}{2}\right)^x$$  

• $$y=\frac{1}{2}\left(10\right)^x$$  

Multiple Choice

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

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

• $$y=\frac{1}{3}\left(3\right)^x$$  

• $$y=9\left(\frac{1}{3}\right)^x$$  

• $$y=3\left(\frac{1}{3}\right)^x$$  

• $$y=\frac{1}{3}\left(9\right)^x$$  

​Sometimes our "b" value is a fraction

​That's ok, let Desmos do all of the work!

​- Just make sure that you push the "/" symbol first.

​- This will create an empty fraction.

​- Then enter your fractions into the top and the bottom.

​For example:

​notice the bigger fraction line

this button will turn your answer into a fraction​

Multiple Choice

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

(Use Desmos to help find the "b" value)

• $$y=3\left(\frac{1}{3}\right)^x$$  

• $$y=3\left(2\right)^x$$  

• $$y=3\left(\frac{1}{2}\right)^x$$  

• y = 3^x

Multiple Choice

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

(Use Desmos to help find the "b" value)

• $$y=2\left(\frac{1}{2}\right)^x$$  

• $$y=\left(\frac{1}{2}\right)^x$$  

• $$y=\left(\frac{1}{3}\right)^x$$  

• $$y=\left(\frac{1}{4}\right)^x$$