{Exponential Growth

Algebra 2

8.1

p. 465

What is a function?

What types of functions have we learned so far?

Review

{

An exponentialfunction involves the expression bx.

{ The base (b) is a positive number other than 1.

An exponentialfunction involves the expression bx.

Graphing Exponential Functions

{

x f(x)

-3 2-3 = 1/8

-2

-1

0

1

2

3

Plug in x.

Plot each point (x, f(x)).

Graphing Exponential Functions

{

x f(x)

-3 2-3 = 1/8

-2 2-2 = 1/4

-1

0

1

2

3

Plug in x.

Plot each point (x, f(x)).

Graphing Exponential Functions

{

x f(x)

-3 2-3 = 1/8

-2 2-2 = 1/4

-1 2-1 = 1/2

0 20 = 1

1 21 = 2

2 22 = 4

3 23 = 8

Plug in x.

Plot each point (x, f(x)).

Graphing Exponential Functions

Graphing Exponential Functions

x f(x)

-3 2-3 = 1/8

-2 2-2 = 1/4

-1 2-1 = 1/2

0 20 = 1

1 21 = 2

2 22 = 4

3 23 = 8

Graphing Calculator Comparisons

1. Graph y = a2x, which has a y-intercept at (0, a).

y = abx-h + k

1. Graph y = a2x, which has a y-intercept at (0, a).

2. Shift the graph vertically kspaces.

y = abx-h + k

1. Graph y = a2x, which has a y-intercept at (0, a).

2. Shift the graph vertically kspaces.

3. Shift the graph horizontally hspaces.

• Note that you are moving opposite the sign in front of h.

y = abx-h + k

{

When something increases by a fixed percent each year (or time period), it can be modeled by the equation:

Exponential Growth

y = a 1+ r( )t

{ a is the initial amount

Exponential Growth

y = a 1+ r( )t

{ a is the initial amount

r is the interest rate

Exponential Growth

y = a 1+ r( )t

{ a is the initial amount

r is the interest rate

t is the time

Exponential Growth

y = a 1+ r( )t