A28­1Notes.notebook
October 27, 2015
Algebra 2
Ch.8 Notes Page 45
P45 8­1 Exploring Exponential Models
Aug 19­6:20 AM
Exponential Functions
y = ab
x
x is a real number
a≠0, b > 0, b ≠ 1 y = (2)3
x
Nov 3­9:22 AM
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A28­1Notes.notebook
October 27, 2015
Growth and Decay y = abx If 0 < b < 1,
b is the Decay Factor
y = (1).5x
If b > 1,
b is the Growth Factor
y = (1)2x
Nov 18­8:38 AM
Population Growth Example
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%. Write a function to model U.S. population growth, in millions, after the year 2000.
(In 2000, there were 281 million people in the U.S.)
(2000 would be year Zero)
Growth Factor (b = 1 + rate of growth)
Nov 18­8:48 AM
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October 27, 2015
Writing an Exponential Function from 2 points
x
y = ab
Given: (2,2) and (3,4)
Solve for a ­ Use (2,2)
Solve for b ­ Use (3,4) and a
Solve for a again ­ Use b
Given: (2,4) and (3,16)
Nov 18­8:52 AM
Decay Example
Basketball Tournament
x
y = ab
64 teams
Single Elimination Tournament
Nov 18­9:01 AM
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A28­1Notes.notebook
October 27, 2015
Depreciation
Loss of Value over Time
y = abx
The initial value of a car is $20,000. After one year the value of the car is about $17,000. Write an Exponential Function to model the situation. Find the value of the car in year 6.
Growth Factor (b = 1 + (r) rate of growth)
r = Final Value ­ Initial Value
Initial Value
Nov 18­9:02 AM
Analyzing a Fuction
y = abx
a is the y­intercept
when x = 0, b0 = 1, so y = a
b indicates if the function is growth or decay
b > 1 Growth 0 < b < 1 Decay
An Asymptote is a line that a graph approaches as x or y increases in absolute value.
y = 0 is a horizontal asymptote
Nov 18­8:59 AM
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A28­1Notes.notebook
October 27, 2015
HW #46
8­1 P434 #1,2,9­11,16­19,24,25,32,35
Please put your name and class period at the top of
the homework. Also include the homework number.
Aug 19­6:25 AM
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