8.1 Exponential
Growth
Algebra II
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. 465
• 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 = ½ 3x
• Plot (0, ½) and (1,
3/2)
• Then, from left to
right, draw a curve
that begins just
above the x-axsi,
passes thru the 2
points, and moves
up to the right
D+
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)
• Connect with a
curve
• Mark asymptote
• D=??
• All reals
• R=???
• All reals < 0
y=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
• AND your
asymptote 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
• R= all reals >1
y=1
Compound Interest
nt
•A=P(1+r/n)
•
•
•
•
•
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 1 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
365
4
≈1000(1.000219)
1
=1000(1.02)
= 1000(1.08)
≈ $1083.28
≈ $1082.43
≈ $1080
Assignment