MAT 212

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• MAT 212
• Brief Calculus

Section 3.1Change, Percent Change, and Average
Rates of Change
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Change New Value Old Value Units output
unitsPercent Change Units percent
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Example After researching several companies, you
and your cousin decided to purchase your first
shares of stock. You bought 200 worth of stock
in one company Your cousin invested 400 in
another. At the end of a year, your stock was
worth 280, whereas your cousins stock was
valued at 500. Who earned more money? Who did
better?
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Change New Value Old Value Units output
unitsPercent Change Units
percent Average Rate of Change Units
output units per input unit
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Average Rate of Change Suppose a large grapefruit
is thrown straight up in the air at t 0
seconds The grapefruit leaves the throwers hand
at high speed, slows down until it reaches its
maximum height, then speeds up in the downward
direction and finally, SPLAT! During the
first second, the grapefruit moves 22 feet
During the next second, the grapefruit moves 12
feet
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Average Rate of Change Use the table to
compute the average rate of change of the
grapefruit over the following intervals 4 t
5 1 t 3 0 t 5
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Average Rate of Change The grapefruits journey
can be modeled by this quadratic function Use
this function to compute the average rate of
change over the following intervals 4 t 5 1
t 3 0 t 5
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Average Rate of Change Graphically, the average
rate of change over the interval a x b is the
slope of line connecting f(a) with f(b). We
refer to this as the secant line Use the graph
of H(t) to compute the average rate of change of
the grapefruit over the following intervals 4 t
5 1 t 3 0 t 5