Algebra 2

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Algebra 2 Ch.8 Notes Page 55 P55 8-1 Exploring
Exponential Models
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Exponential Functions
y abx
x is a real number a?0, b gt 0, b ? 1
y (2)3x
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Growth and Decay y abx
If 0 lt b lt 1, b is the Decay Factor y (1).5x
If b gt 1, b is the Growth Factor y (1)2x
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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)
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Writing an Exponential Function from 2 points
y abx
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)
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Decay Example
y abx
Basketball Tournament
64 teams Single Elimination Tournament
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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
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Analyzing a Fuction
y abx
a is the y-intercept when x 0, b0 1, so y
a b indicates if the function is growth or
decay b gt 1 Growth 0 lt b lt 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
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HW 60 8-1 P434 1,2,9-11,16-19,24,25,32,35 Plea
se put your name and class period at the top
of the homework. Also include the homework
number.