Lesson 8.1 Exponential Models.notebook
March 26, 2012
8.1 - Exploring Exponential Models
Objective: Be able to use equations and graphs
to model exponential growth and decay
Exponential Function:
initial value
exponent
(y­intercept)
(how many times it grows or decays)
y = a(bx)
growth/decay factor
(how much it increases or decreses by)
Exponential Growth vs. Decay
Exponential Function:
y = a(b)x
Graph the following two exponential functions in your graphing calculator:
a) what is the y­interecept for both equations?
b) Which one has a growth rate and which one has a decay rate? What are they?
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Lesson 8.1 Exponential Models.notebook
March 26, 2012
Graphing exponential growth (b > 1)
Initial value: ______
Growth Factor: ______
x y
Graphing exponential growth (b > 1)
Initial value: ______
Growth Factor: ______
x y
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Lesson 8.1 Exponential Models.notebook
March 26, 2012
Graphing exponential growth (b > 1)
Initial value: ______
Growth Factor: ______
x y
Graphing exponential decay (b < 1)
Initial value: ______
Decay Factor: ______
x y
3
Lesson 8.1 Exponential Models.notebook
March 26, 2012
Graphing exponential decay (b < 1)
Initial value: ______
Decay Factor: ______
x y
Graphing exponential decay (b < 1)
Initial value: ______
Decay Factor: ______
x y
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Lesson 8.1 Exponential Models.notebook
Exponential Growth
2(1.3)x
x
100(5)
.25(3)x
March 26, 2012
Exponential Decay
3(.25)x
1 x
3( )
3
.75x
130x
When given the rate of increase you can find the growth/decay
factor using b = 1 + r (remember, y = abx)
In 2000, the annual rate of increase in the U.S. population was about 1.24%
Suppose the rate of increase continues to be 1.24%. Create a function to model the U.S. population growth in millions after the year 2000. Use your function to predict the population in the year 2015. 5
Lesson 8.1 Exponential Models.notebook
March 26, 2012
When given the rate of increase you can find the growth/decay
factor using b = 1 + r (remember, y = abx)
You decide you're going to buy a new car. The initial value of the car is $20,000. The instant you drive it off of the lot, the value of the car depreciates by 15% per year. Create a function to model the depreciation of the car after x number of years. Use your function to predict the value of the car after you've had it for six years. 2 practice problems due before you leave!
Homework #18
VIDEOS @ www.phschool.com
Web code age-0801
Watch video 1 and 3 (optional)
Web code age-0802
Watch both videos (required)
PROBLEMS to complete
Pg 434 #9, 45a Pg 442 #3, 7, 9, 12, 14, 15
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