DO NOW:YOUR PARENTS HAVE DECIDED TO CHANGE YOUR ALLOWANCE AND YOU MUST DECIDE WHICH PLAN

WILL GIVE YOU MORE MONEY NEXT MONTH.

PLAN A – ON THE FIRST DAY YOU WILL RECEIVE 1 CENT, THE SECOND

DAY 2 CENTS, THE THIRD DAY 4 CENTS…..AND SO ON…EACH DAY

THE AMOUNT OF MONEY YOU RECEIVE WILL DOUBLE.

PLAN B – YOU WILL RECEIVE $100 EACH DAY.

Objective: By then end of class today, I will be able to graph exponential functions.

PLAN A – IS AN EXAMPLE OF AN EXPONENTIAL FUNCTION

Exponential Functions

An exponential function is a function of the form:

where x is always the exponent

xy a b

EXPONTENTIAL FUNCTIONS

Compound interest Some populations increase at a

rate of 2 % each year. Radioactive half-life Bacteria growing Vehicles or something loses value

at a rate of 11% per year

First, let’s take a look at an exponential function

2xy x y = 2x y

0 20 1

1 21 2

2 22 4

-1 2– 1 1/2

-2 2– 2 1/4

What is the y-intercept of this graph?Answer: The y-intercept is 1.

9322

3311

1300

3–1–1

y3xx

Graph y = 3x from –1 ≤ x ≤ 2

Answer: The y-intercept is 1.

Graph y = 5x from –2 ≤ x ≤ 2 and find the

y-intercept

x y = 5x y

-2 5– 2 1/25

-1 5– 1 1/5

0 50 1

1 51 5

2 52 25

LET’S GRAPH THE FOLLOWING: y = 4X

y = 15X

Then make 4 conclusions about your graphs.

•Y-intercept always = 1

•Graph is above the x – axis

•The greater b, the steeper the graph

•The graph will never touch the x-axis

Next, observe what happens when b assumes a value such that

0<b<1.Graph each in your calculator and sketch:

x

x

x

y

y

y

8

1

4

1

2

1What is different

about these graphs?

What is similar?

10

8

6

4

2

-5 5 10

h x = 1

8

x

g x = 1

4

x

f x = 1

2

x

This is what your graphs should look like.

Now on the same graph – graph the following

x

x

y

y

3

1

3 What do you notice?

Our general exponential form is “b” is the base of the function and

changes here will result in:

When b>1, the graph increases.

When 0<b<1, the graph decreases.

y a b x