9-1 Exponential Functions Review

9-1 Exponential Functions Review

Open Ended

Let's check in!

If how you are feeling today was a color, what color would you be?

Give an explanation too! (all answers are anonymous) 

​Let's start off with a video reminding us of what exponential functions are.

​https://www.youtube.com/watch?v=tAaDItpC8OI

​

Poll

After watching the video, how do you feel about your knowledge of exponential functions? (It's okay not to be a pro yet!)

• I feel amazing! I can't wait to practice more and help others learn this material

• I feel good. It will take more examples and practice but I believe in myself!

• I feel alright. I have slight confidence in myself to learn and understand exponential functions

• Not too hot. I am nervous for exponential functions

Does the data display exponential behavior?

• ​Make sure that the domain values are at regular intervals (example: 1, 2, 3, 4 OR 6, 12, 18, 24)

​No! The domain is decreasing in a regular interval BUT the range is not multiplying by the same number each time. (It's subtracting 20 each time instead)

• ​Check that the range has a common factor (multiplies by the same number each time)

Multiple Choice

What function model best represents the data in the table?

• linear

• exponential

Multiple Choice

What function best models the data in the table?

• linear

• exponential

Multiple Choice

Since a picture frame includes a border, the picture must be smaller in area than the entire frame. The table shows the relationship between picture area and frame length for a particular line of frames. Is this an exponential relationship?

• Yes, there is a common factor between the picture areas

• No, there is not a common factor between the picture areas

​Exponential Growth

​Example of Exponential Growth

Multiple Choice

Consider the equation  $$y=3^x$$  , what is the domain and range of the function?

• D=All real numbers

  R=y>0

• D=y>0

  R=All real numbers

• D=x>0

  R=y>0

• D=x>0

  R=All real numbers

Multiple Choice

Consider the equation  $$y=3^x$$  , where is the asymptote?

• x=0

• y=3

• y=0

• x=3

Multiple Choice

Choose the correct graph of $$y=3^x$$  

​Exponential Decay

​Example of Exponential Decay

Multiple Choice

Is the pictured graph growth, decay, or linear or none?  

• Exponential Growth
• Exponential Decay
• Linear
• None

Multiple Choice

Which represents exponential decay?

• A

• B

• C

• D

Multiple Choice

In an exponential function, what does the 'a' represent? 

• SLOPE
• RATE OF CHANGE
• Y-INTERCEPT
• COMMON RATIO

Multiple Choice

Which of the following is an increasing exponential function whose y-intercept is 50?

• y = 50(.05)^x
• y = 50x - 4
• y = (2)^x + 50
• y = 50(1.4)^x

Multiple Choice

The expression 12(1.015)^t models the population of elephants in a wildlife refuge after t years since 1975.
Is the population of elephants increasing or decreasing?

• Increasing
• Decreasing

Multiple Choice

The expression 12(1.015)^t models the population of elephants in a wildlife refuge after t years since 1975.
What does the value 12 represent?

• The predicted increase in number of elephants in the refuge each year.
• The predicted decrease in number of elephants in the refuge each year.
• The number of years it will take for the elephant population to stop increasing.
• The initial amount of elephants in the park.

Multiple Choice

The expression 12(1.015)^t models the population of elephants in a wildlife refuge after t years since 1975.
What does the value 1.015 represent?

• The number of elephants was 1,015 in 1975.
• The number of elephants increases by 1.5% each year.
• The number of elephants increases by 101.5% each year.
• The number of elephants is multiplied by 1.015 each year.

Multiple Choice

The amount of downloads for an album on iTunes, g(d), where d is the number of days since the album was first uploaded can be represented as
g(d) = 5^1.5d
How many downloads will the album have after 3 days?

• 125
• 11
• 1398
• 140

Multiple Choice

Which function represents the table of values?

• f(x) = 4x

• f(x) = x³

• f(x) = 4^x

• f(x) = 4^x-1

Multiple Choice

Which table represents the following equation?

Multiple Choice

This is the horizontal line which the values of the function cannot fall below :

• Asymptote

• Growth Factor

• Axis of symmetry

• Curve

Poll

After todays review, how do you feel about your knowledge of exponential functions? (It's okay not to be a pro yet!)

• I feel amazing! I can't wait to practice more and help others learn this material

• I feel good. It will take more examples and practice but I believe in myself!

• I feel alright. I have slight confidence in myself to learn and understand exponential functions

• Not too hot. I am nervous for exponential functions