Essential Skills: Graph Exponential FunctionsIdentify behavior that displays exponential functions

An exponential function is a function that can be described by an equation in the form y = abx

Conditions: a ≠ 0, b ≠ 1, and b > 0 Examples:▪ y = 2(3)x

▪ y = 4x

▪ y = (½)x

Example 1: Graph y = 4x. Find the y-intercept and state the domain and range Make a table of x-values (your choice)

and fill in the chart.▪ Advice▪ Always choose x = 0 (the y-int)▪ Choose at least one positive and

one negative number

x 4x y

-1 4-1 ¼

0 40 1

1 41 4

2 42 16

Example 1: Graph y = 4x. Find the y-intercept and state the domain and range Plot each point from

your table Connect your points

with a smooth line

The domain (x-values) are allreal numbers

The range (y-values) are all positive real numbers

x 4x y

-1 4-1 ¼

0 40 1

1 41 4

2 42 16

Example 1: y = 4x

Estimate the value of 41.5

Calculator: 4^(1.5) = 8

Graphing Exponential Growth Example: Graph y = 3 ● 2x

Step 1: Make a table of values Step 2: Graph the coordinates with a smooth curve

x 3 ● 2x y

-2 3 ● 2-2 3/4 = 0.75

-1 3 ● 2-1 3/2 = 1.5

0 3 ● 20 3

1 3 ● 21 6

2 3 ● 22 122 4–2–4 x

2

4

6

8

y

Example 2: y = 5x

Estimate the value of 50.25

About 1.5

Graphing Exponential Growth Example: Graph y = ¼x

Step 1: Make a table of values Step 2: Graph the coordinates with a smooth curve

▪ On board

Example 3: y = ¼x

Estimate the value of ¼-1.5

About 8

Assignment Page 427 1 – 5, 11 – 19 (odds)

Essential Skills: Graph Exponential FunctionsIdentify behavior that displays exponential functions

Exponential growth y = a ● bx

Note that this is the same as any exponential function, except that the base in exponential growth is always greater than 1.

Why?

Starting amount(when x = 0)

Base (greater than 1)

Exponent

Exponential decay y = a ● bx

Note that this is the same as exponential growth, except the base is between 0 and 1.

Why?

Starting amount(when x = 0)

Base (between 0 and 1)

Exponent

Example 3 Some people say that the value of a new car

decreases as soon as it’s driven off the dealer’s lot. The function V = 25,000(0.82)t models the depreciation of the value of a new car that originally cost $25,000. V represents the value of the car and t represents the time in years from the time the car was purchased. What is the value of the car after five years?

V = 25000(0.82)t

▪ t = 5 years▪ V = 25000(0.82)5

▪ V ≈ $9268

Your Turn The function V = 22,000(0.82)t models

the depreciation of the value of a new car that originally cost $22,000. V represents the value of the car and t represents the time in years from the time the car was purchased. What is the value of the car after one year?

V ≈ $18,040

Example 4 Determine whether the set of data displays

exponential behavior. Explain why or why not.

Look for a pattern▪ The domain increases by regular intervals of 10▪ Look for a common pattern among the range▪ 10 25 62.5

156.25

x2.5 x2.5 x2.5▪ Since the range values have a common factor, the

equation for the data may involve (2.5)x, and the data is probably exponential.

x 0 10 20 30

y 10 25 62.5 156.25

Your Turn Determine whether the set of data

displays exponential behavior. Explain why or why not.

▪ Yes, the data is exponential▪ Each range value is being multiplied by 0.5

x 0 10 20 30

y 100 50 25 12.5

Assignment Page 427▪ 7 (part b only), 8, 9▪ 20 (part a only), 21 - 24