Sec 3.1.2 What is the Connection Multiple Presentations This template can be used as a starter file to give updates for project milestones. Sections Right-click on a slide to add sections. Sections can help to organize your slides or facilitate collaboration between multiple authors. Notes Use the Notes section for delivery notes or to provide additional details for the audience. View these notes in Presentation View during your presentation. Keep in mind the font size (important for accessibility, visibility, videotaping, and online production) Coordinated colors Pay particular attention to the graphs, charts, and text boxes. Consider that attendees will print in black and white or grayscale. Run a test print to make sure your colors work when printed in pure black and white and grayscale. Graphics, tables, and graphs Keep it simple: If possible, use consistent, non-distracting styles and colors. Label all graphs and tables.

Review Topics: find the unknown. 5 min No need to use a calculator! 2 𝑥+3 = 2 2𝑥 3 2𝑥+1 = 3 𝑥 a bit more challenging: 3) 9 𝑥 = 3 40 4) 8 60 = 2 𝑥

General form of an exponential function What each part represents Before we start; review you notes and make sure to have the following information: General form of an exponential function What each part represents Difference between when b>1 and when 0<b<1 If b<0 then the function is no longer, exponential.

What exponential functions and their graphs have in common: Domain: −∞<𝒙<∞ OR x is all real numbers Range: y>0 The general shapes of the curves are the same. The line y=0 is the asymptote. The y-intercept is (0,a)

Different Models Table Rule or equation Graph Context

Exponential Functions Once one of the representations is given, you should be able to determine the other 3 representations. #3-22on page 122, displays an example of each kind. Please take careful notes as you cover each example.

I) #3-22 a) Table of values is given Copy the table below: Determine the other 3 representations. Graph Rule Context Bounce Number Height cm 1 2 84.5 3 67.6 4 54.1 Pg 122 #3-22

Finding the Rule: The general equation: 𝑦=𝒂 𝑏 𝑥 Determine the multiplier… i.e. the value of b. Determine the initial value i.e. 𝒂 , in this the initial height. State the rule

Finding the Rule: Without a graphing calculator Finding the Rule: Without a graphing calculator. The general equation: 𝒚=𝒂 𝒃 𝒙 Bounce Number Height cm 1 2 84.5 3 67.6 4 54.1 Find the common multiplier, b: 𝑏= 67.6 84.5 =0.8 Find a by working backwards: 𝑎~132 84.5 multiplied by what value=67.6 The final rule or equation is 𝑦=132∙ 0.8 𝑥

A second method to find the value of a. Choose one of the given points… for example (2, 84.5) Then: 𝑦=84.5 (0.8) 𝑥−2 Now sub x=0 in the above function 𝑦=84.5 (0.8) 0−2 𝑦=84.5 (0.8) −2 𝑦 ~ 132 So the initial value, when x=0, is 132. You can also use either of the other two given points.

Check your answer Generate a table of values on your calculator using your rule. Compare the table on your calculator to the given table.

Finding the Rule: The general equation: 𝑦=𝒂 𝑏 𝑥 What if consecutive x values are not given? What if the values close to the y intercept is not known? We will revisit these issues later.

II) #3-22 b) Context is given. Read the problem, and then discuss the answer in your group.

III) #3-22 C) Table of values is given Day Uninfected computers 27 1 18 2 12 3 8 Generate a rule Generate a graph

Find the rule to model the exponential growth; then graph the model. Your Turn: x y 1 2 360 3 432 4 Find the rule to model the exponential growth; then graph the model.

Answer: 𝑦= 250(1.2) 𝑥 OR 𝑦= 250( 6 5 ) 𝑥

Review and Preview Page 123 # 26-33 Homework Extra Credit Opportunity: If you do any activity to observe Veteran’s Day, let me know and I will give you extra credit.