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{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