7.1 Exponential Growth
Vocabulary:
-exponential function:
-exponential growth function:
-growth factor:
-domain of an exponential function:
-horizontal asymptote:
-range of an exponential function:
Feb 7­11:54 AM
Examples: Graph the function. State the domain and
range.
1.) y = 2x
x
y
2.) y = 2x + 2
x
y
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3.) y = -3x
x
y
4.) y = 2 3x-1 - 2
x
y
Feb 7­1:42 PM
Exponential Growth Models: When a real-life
quantity increases by a fixed percent each year (or
other time period), the amount y of the quantity
after t years can be modeled by the equation:
_____________, where
a=
r=
t=
Example: In 1996, there were 2573 computer
viruses and other computer security incidents.
During the next 7 years, the number of incidents
increased by about 92% each year. Write an
exponential model that describes the situation.
Feb 7­1:43 PM
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Compound Interest Formula:
P=
r=
n=
t=
Values for n:
n = 1:
n = 2:
n = 4:
n = 12:
n = 365:
Example: You deposit $4000 in an account that pays
2.92% annual interest. Find the balance after 3 years
if the interest is compounded with the given
frequency.
a.) Quarterly
b.) Daily
Feb 7­1:51 PM
Example: Each March from 1998 to 2003, a website
recorded the number y of referrals it received from
Internet search engines. The results can be
modeled by y = 2500(1.50)t where t is the number of
years since 1998.
a.) Identify the initial amount, the growth factor
and the annual percent increase.
b.) Graph the function and state the domain and
range. Use the function to estimate the number of
referrals the website received from search engines
in March of 2002
7.1 Homework: pages 482-483 #6, 8, 17, 23, 25, 28, 30, 35, 37
Feb 7­2:06 PM
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7.2 Exponential Decay
Vocabulary:
-exponential decay function:
-decay factor:
Examples: Tell whether each function represent
exponential growth or exponential decay.
1.) y = 2(3)x
2.) y = 4(¼)x
3.) y = 3(7/2)x
4.) y = ¼(4)x
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Examples: Graph. State the domain and range.
1.) y = (½)x
x
y
2.) y = -(¼)x + 2
x
y
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3.) y = 6(½)x+5 - 2
x
y
Exponential Decay Models: When a real-life quantity
decreases by a fixed percent each year (or other
time period), the amount y of the quantity after t
years can be modeled by the equation _________,
where a =
r=
t=
Feb 7­2:18 PM
Example: A new snowmobile costs $4200. The value
of the snowmobile decreases by 10% each year.
a.) Write an exponential decay function that models
the situation.
b.) Use the model to determine the value of the
snowmobile after 3 years.
c.) Use the graph to estimate when the value of the
snowmobile will be $2500.
7.2 Homework: Pages 489-490: #3-6, 8, 16, 23, 31
Feb 7­2:21 PM
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