8­1 Exploring exponential models
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8­1 Exploring Exponential Models
Objective: Model exponential growth and decay.
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Check Skills You'll Need
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8­1 Exploring exponential models
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An exponential function is a function
with the general form y = abx, where x is a real number, a ≠0, b > 0, and b ≠ 1.
You can use an exponential function
with b > 1 to model growth. When b > 1, b is the growth factor.
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Graph y = 2x.
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x
Graph the exponential function y = 3
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x
Graph the exponential function y = 4(2)
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8­1 Exploring exponential models
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Second, find a, the initial population.
In 2000, the population was 281, so a = 281.
Next, write the exponential function.
y = 281(1.0124)x
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y = 281(1.0124)x
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You can use an exponential function with 0 < b < 1 to model decay.
When b < 1, b is a decay factor.
An asymptote is a line that a graph approaches as x or y increases in absolute value.
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Without graphing, determine whether each function represents exponential growth or exponential decay.
a. y = 100(0.12)x
b. y = 0.2(5)x
c. y = 16(½)x
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Graph y = 24(1/2)x. Identify the horizontal asymptote.
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Graph the decay function. Identify the horizontal asymptote.
y = 24(1/2)x
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Homework
p. 434
# 1­3, 9­12, 16­22
Day 2 homework
page 435
#'s: 24­54 multiples of 3, 58
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