1. Tuesday April 15, 2014 7.1 Exponential Growth Functions
Objective: To solve and graph polynomial and radical functions
EQ: Can you graph an exponential function?
What is an exponential function?
An exponential function has the form of y = abx, a ≠ 0, b is a positive number other than 1
Example: y = 2x or y =(½) x
There are 2 kinds of exponential function:
1. Exponential growth: b > Example: y = 4x
2. Exponential decay : 0 < b < 1 Example: y =(⅛) x
Exponential Growth Function:
Domain: all real numbers
Range: y > 0
To graph:
Step 1: Plot 2 points (0, a) and (1, b)
Step 2: Find couple points left of (0, a) and right to (1, b)
Step 3: Make a smooth curve, the left of the curve never crosses x axis
Example 1: Graph y = 2x
Solution:
a = 1, b = 2
Step 1: Plot 2 points (0, 1) and (1, 2)
Step 2: Points left of (0, 1) , right of (1, 2)
Step 3: Make a smooth curve

2. Tuesday April 15, 2014 7.1 Exponential Growth Functions Example:
Solution:
Practice:
Solution:

3. Tuesday April 15, 2014 7.1 Exponential Growth Functions
Exponential Growth Models: y = a (1+r) t
a = initial amount, r = % (in decimal form), t = time
Example: In 1996, there were 2573 computer viruses security incidents. During the next 7 years, the number of incidents increased by 92% per year.
Write the exponential growth model giving the number n of incidents t years after 1996
Graph the model
Use the graph to estimate the year when there were about 125,000 computer security incidents
Solution:

4. Tuesday April 15, 2014 7.1 Exponential Growth Functions Translations
To graph a function of the form y = abx-h +k:
sketch y = abx
then translate:
h units horizontally and
k units vertically
Example: y = 4. 2x-1 – 3
Graph y= 4. 2x
a = 4, b=2
h = 1, k = -3
Example : Graph the function. State the domain and range
y = 4x 2. y = ½ 3x 3. y = 3x-1 – 3
Exponential Growth Models: y = a (1+r) t
a = initial amount, r = % (in decimal form), t = time
Example: In 1996, there were 2573 computer viruses security incidents. During the next 7 years, the number of incidents increased by 92% per year.
Write the exponential growth model giving the number n of incidents t years after 1996
Graph the model
Use the graph to estimate the year when there were about 125,000 computer security incidents
Solution:

5. Wednesday April 23, 2014 7.2 Exponential Decay Functions
Objective: To solve and graph polynomial and radical functions
EQ: Can you graph an exponential function?
Exponential Decay Function has the form of f (x) = of y = abx, where 0 < b < 1
Domain: all real numbers
Range: y > 0
To graph:
Step 1: Plot 2 points (0, a) and (1, b)
Step 2: Find couple points left of (0, a) and right to (1, b)
Step 3: Make a smooth curve, the left of the curve never crosses x axis
Example 1: Graph y = (1/2)x
Solution:
a = 1, b = 1/2
Step 1: Plot 2 points (0, 1) and (1, 1/2)
Step 2: Points left of (0, 1) , right of (1, 1/2)
Step 3: Make a smooth curve

6. Wednesday April 23, 2014 7.2 Exponential Decay Functions Example:
Translations

7. Tuesday April 15, 2014 7.2 Exponential Growth Functions
Exponential Decay Models: y = a (1 - r) t
a = initial amount, r = % (in decimal form), t = time
Example: A snowmobile costs $ The value of the snowmobile decreases by 10% each year.
Write the exponent decay model?
Find the value after 3 years
Graph the model
Find when the value of the snowmobile will be $2500
Solution:

8. Thursday April 24, 2014

9. Thursday April 24, 2014 7.3 Exponential Growth Functions
Objective: To solve and graph polynomial and radical functions
EQ: Can you graph an exponential function?
What is the Euler number or the Natural Base e?
Example:

10. Thursday April 24, 2014 7.3 Exponential Growth Functions
Calculating Compounded Interest?
Example: You have a $4,000,000 in an account that pay 6% annual interest compounded continuously. What is the balance after 1 year?
Solution:
Compound annually A = P [1+ (.06)] =
Compound quarterly A = P [1+ (.06/4)] 06(4) =
Compound monthly A = P [1+ (.06/12)] 06(12) =
Compound daily A = P [1+ (.06/365)] 06(365) =
Compound continuously: A = Pert = 4000e.06(1) =

11. Friday May 2, 2014
Rewrite the followings in exponential form
(use whole numbers, both positive or negative)
8 =
0 =
12 =
¼ =

12. Thursday April 24, 2014 7.4 Evaluate and Graph Logarithm Functions
Objective: To solve and graph polynomial and radical functions
EQ: How do exponent and logarithm functions relate?
Definition
Example:
Example:

13. Thursday April 24, 2014 7.4 Evaluate and Graph Logarithm Functions
Inverse Functions:
f(x) = bx is the inverse function of g(x) = logbx
Therefor:
Example:
Example:

14. Thursday April 24, 2014 7.4 Evaluate and Graph Logarithm Functions
Parent Graphs for Logarithmic Functions:
Example:

15. Thursday April 24, 2014 7.4 Evaluate and Graph Logarithm Functions
Translations in Logarithmic Function Graph:
From the parent function: y = logb x to y = logb (x – h) + k
(the graph moves h units to the right and k units up)
Example: y = logb (x + 3) + 1
Solution: