# 8 1 Exponential Growth

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p. 478
7.1 Exponential Growth
What you should learn:

Goal 1 Graph and use Exponential Growth
functions.

Goal 2      Write an Exponential Growth model
that describes the situation.

A2.5.2
7.1 Graph Exponential Growth Functions
Exponential Function

• f(x) = bx where the
base b is a positive
number other than
one.
• Graph f(x) = 2x
• Note the end behavior
• x→∞ f(x)→∞
• x→-∞ f(x)→0
• y=0 is an asymptote
Asymptote
• A line that a graph approaches as you move
away from the origin
The graph gets closer
and closer to the line
y = 0 …….
But NEVER reaches it

2 raised to any power
Will NEVER be zero!!

y=0
Lets look at the activity on p. 479

•   This shows of y = a * 2x
•   Passes thru the point (0,a) (the y intercept is a)
•   The x-axis is the asymptote of the graph
•   D is all reals (the Domain)
•   R is y > 0 if a > 0 and y < 0 if a < 0
•   (the Range)
• These are true of:
• y = abx
• If a > 0 & b >1 ………
• The function is an Exponential
Growth Function
Example 1
• Graph y   3
1   x
2

• Plot (0, ½) and (1, 3/2)
• Then, from left to
right, draw a curve
that begins just above
the x-axis, passes thru
the 2 points, and
moves up to the right
D= all reals
R= all reals>0

y=0

Always mark asymptote!!
Example 2
• Graph y = - (3/2)x
• Plot (0, -1) and
(1, -3/2)            y=0
• Connect with a
curve
• Mark asymptote
• D=??
• All reals
• R=???
• All reals < 0
To graph a general Exponential Function:

• y = a bx-h + k
• Sketch y = a bx
• h = ??? k = ???
• Move your 2 points h units left or right …
and k units up or down
• Then sketch the graph with the 2 new points.
Example 3
Graph y = 3·2x-1 - 4

• Lightly sketch y = 3·2x
• Passes thru (0,3) &
(1,6)
• h= 1, k= -4
• Move your 2 points to
the right 1 and down 4
k units (4 units down
in this case)
D= all reals
R= all reals
>-4

y = -4
Now…you try one!

• Graph y = 2·3x-2 +1
• State the Domain and
Range!
• D= all reals
y=1
• R= all reals >1
Compound Interest

A=P(1+r/n) nt
   P - Initial principal
   r – annual rate expressed as a decimal
   n – compounded n times a year
   t – number of years
   A – amount in account after t years
Compound interest example
• You deposit \$1000 in an account that pays
8% annual interest.
• Find the balance after I year if the interest is
compounded with the given frequency.
• a) annually b) quarterly          c) daily

A=1000(1+ .08/1)1x1 A=1000(1+.08/4)4x1 A=1000(1+.08/365)365x1
= 1000(1.08) 1      =1000(1.02)4       ≈1000(1.000219)365
≈ \$1083.28
≈ \$1080             ≈ \$1082.43
Assignment

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