By Thersia Weber and Rachel Eron
Only an exponential function
if the x is in the exponent.
f(x) = abx
a = initial amount
b = rate of growth/base
x = variable
b > 1: exponential growth
b < 1: exponential decay
f(x) = 3x
Exponential
Function?
Yes
X is in exponent
Initial Value?
1
A isn’t listed, automatically 1
Base?
3
B=3
Growth or Decay?
Growth
B=3 > 1
f(x) = 4x7
Exponential Function?
No
X isn’t in exponent
Initial Value?
-
Base?
-
Growth or
Decay?
-
a=x=0
then plug it into y=abx
Power
y=6bx
x
f(x)
-2
96
-1
24
0
6
1
3/2
2
3/8
then plug in another
value on the table
3/2 = 6b1
solve for b
b= 3 . 1
2 6
b= 3 = 1
12 4
plug b into equation
y= 6(1/4)x
x
f(x)
-2
108
-1
36
0
12
1
2
x
f(x)
1900
4.8
1910
5.6
1920
6.5
4
1930
7.6
4/3
1940
7.9
1950
8.7
1960
10.1
1970
11.1
y = abx
y = 12bx
4 = 12b1
4/12 = b
4/12 = 1/3 = b
y = 12 (1/3)x
y = 12 (1/3)x
y = abx
y = 4.8bx
5.6 = 4.8b10
1.167 = b10
ln 1.167 = 10 ln b
ln b = .0154
b = e.0154
y = 4.8 e.0154x
y = 4.8 e.0154x
Graph transformations previously learned also apply to exponential functions
Horizontal Translations
y = abx-c graph shifts to right
y = abx+c graph shifts to left
Vertical Translations
y = abx +c graph shifts up
y = abx-c
graph shifts down
Axis Flips
y = ab-x graph flips over y axis
y = -abx graph flips over x axis
Use URL to explore transformations of
Exponential functions on graph
http://www.explorelearning.com/index.cfm?method=cR
esource.dspView&ResourceID=104#
Exponential equations can be found in many real life
situations.
To solve real life equations, look at it as y = abx and find
initial amount and other variables.
Plug in the numbers given and find the information asked
for in problem.
The number B of bacteria in a petri dish culture of t hours is given by:
B = 100e0.693t
Find initial number of bacteria present.
How many bacteria are present after 6 hours?
B = 100e0.693t
B = 100e0.693x6
B = 6394
Initial: 100
# Present after 6 hours: 6394
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Suppose your parents are going to pay you a weekly allowance
for doing your household chores this coming year. Also, imagine
that they are going to give you a choice of two payment
schemes. With Choice A, your parents will pay you $10 every
week. Therefore, you will have earned $10 after the first week,
$20 after the second week, $30 after the third week, and so on.
With Choice B, just to be nice, they are going to pay you $0.01
before you even start working. After you complete chores for
week one, they will double your money, thus giving you a total of
$0.02. After you complete chores for week two, they will once
again double your money, thus giving you a total of $0.04. They
will continue to double your money at the end of every week.
Write an equation for each payment scheme and use
www.graphsketch.com to make graphs. Explain which payment
scheme you will choose and why using the graphs.
Each project will be turned in and graded according to rubric,
worth 20 points.

Each payment scheme will give you a fair
amount of allowance, but judging by the
graphs, the second payment plan would be a
better choice because you will earn more
eventually, faster.
2-3 groups to present
explanation.
If present, 5 extra
credit points.
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Precalculus Textbook by Franklin Demana,
Bert Waits, Bregory Foley, and Daniel Kennedy
www.graphsketch.com (Graph, slide 10)
http://www.explorelearning.com/index.cfm?
method=cResource.dspView&ResourceID=10
4# (Graphing Activity, slide 7)
http://www.cartoonstock.com/directory/e/ex
ponential_growth.asp (Introduction Comic)
http://education.ti.com/calculators/downloa
ds/US/Activities/Detail?id=7727
(Supplemental Activity, Allowance)
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Now take a 10 question assessment on what
you’ve learned.
Assessment
Assessment Answers