1. Sec 3.1.2 What is the Connection
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2. 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) 𝑥 = 3 40
4) = 2 𝑥

3. 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.

4. 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)

7. Different Models
Table
Rule or equation
Graph
Context

8. 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.

9. 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

11. 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

12. 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= =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

13. 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.

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

15. 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.

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

17. 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

20. 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.

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

23. 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.