1. 7.1 Exponential Growth p. 478 What you should learn: Goal 1
Graph and use Exponential Growth functions.
Write an Exponential Growth model that describes the situation.
Goal 2
A2.5.2
7.1 Graph Exponential Growth Functions

2. 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

3. 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

4. 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)

5. These are true of:
y = abx
If a > 0 & b >1 ………
The function is an Exponential Growth Function

6. Example 1 Graph 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

7. D= all reals
R= all reals>0
y = 0
Always mark asymptote!!

8. 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

9. 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.

10. 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)

11. D= all reals
R= all reals
>-4
y = -4

12. Now…you try one! Graph y = 2·3x-2 +1 State the Domain and Range!
D= all reals
R= all reals >1
y=1

13. A=P(1+r/n)nt Compound Interest 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

14. 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
= 1000(1.08)1
≈ $1080
A=1000(1+.08/4)4x1
=1000(1.02)4
≈ $
A=1000(1+.08/365)365x1
≈1000( )365
≈ $

15. Assignment