8.1 Exponential Growth 8.2 Exponential Decay

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8.1 Exponential Growth8.2 Exponential Decay
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Exponential Function
An exponential function has a positive base other
than 1.
The general exponential function is
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The graph of y bx
GraphExponential function.tii
Asymptote a line that a graph approaches as you
move away from the origin. ( The graph never
touches the line.)
If b is greater than 1 the graph is an
exponential growth. b gt 1
If b is greater than 0 but less than 1 the graph
is an exponential decay. 0 lt b lt 1 ( A
reflection in the y direction.)
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The graph of y abx-h k
GraphExponential function.tii
If a is negative the graph will reflect in the x
direction. The absolute value of a changes the y-
intercept.
The h shifts the graph horizontally. (left or
right)
The k shifts the graph vertically. (up or down)
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Exponential Growth Model
Instead of x, t is the variable.
(1r) is called the growth factor.
a is the initial amount. y is the amount after
t years.
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Exponential GrowthCompound Interest
A is the balance. P is the principal deposited in
an account. r is the interest rate changed to a
decimal ( ? 100). n is the number of times the
interest is compounded in a year. Annually
n 1 Semiannually n 2
Quarterly n 4 Monthly n
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Compound Interest Problem
You deposit 500 in an account that pays 3
interest. Find the balance after 2 years if the
interest is compounded quarterly.
A ? P 500
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Exponential Decay Model
y is the quantity after t years. t is the
variable. a is the initial amount. (1-r) is the
decay factor.
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Exponential DecayDepreciation
You buy a new car for 22,000. The value of the
car decreases by 12.5. What is the value of the
car after 4 years.
y ? a 22,000