Over Lesson 7–4

What is 3,352,000 in scientific notation?

What is 0.00000281 in scientific notation?

What is 3 × 104 in standard form?

What is 6.12 × 10–5 in standard form?

Over Lesson 7–4

2.81 × 10–6

3 × 108

30,000

0.0000612

3.352 × 106

Answers

Exponential Functions

Lesson 7-5

Understand how to use multiplication and division properties of exponents with rational exponents and how to multiply and divide numbers written in scientific notation.

LEARNING GOAL

VOCABULARY

Graph with a > 0 and b > 1

A. Graph y = 4x. Find the y-intercept and state the domain and range.

Graph the ordered pairs and connect the points with a smooth curve.

Answer: The graph crosses the y-axis at 1, so the y-intercept is 1. The domain is all real numbers and the range is all positive real numbers.

Graph with a > 0 and b > 1

B. Use the graph of y = 4x to determine the approximate value of 41.5.

The graph represents all real values ofx and their corresponding values of y for y = 4x.

Answer: The value of y is 8 when x = 1.5.

Use a calculator to confirm this value.

41.5 = 8

A. Graph y = 5x.

x y

-1

0

1

2

3

B. Use the graph of y = 5x to determine the approximate value of 50.25.

Graph with a > 0 and 0 < b < 1

Graph the ordered pairs and connect the points with a smooth curve.

Answer: The y-intercept is 1. The domain is all real numbers and the range is all positive real numbers.

A. Find the y-intercept and state

the domain and range.

Graph with a > 0 and 0 < b < 1

Use a calculator to confirm this value.

Answer: The value of y is about 8 when x = –1.5.

A. Graph

A. $21,000

B. $23,600

C. $18,040

D. $20,000

B. DEPRECIATION The function V = 22,000 ● 0.82t 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?

Identify Exponential Behavior

Determine whether the set of data displays exponential behavior. Explain why or why not.

Method 1 Look for a pattern.

The domain values are at regular intervals of 10. Look for a common factor among the range values.

10 25 62.5 156.25

× 2.5 × 2.5 × 2.5

Identify Exponential Behavior

Method 2 Graph the data.

Answer: The graph shows rapidly increasing values of y as x increases. This is a characteristic of exponential behavior.

Answer: Since the domain values are at regular intervals and the range values differ by a positive common factor, the data are probably exponential. The equation for the data may involve (2.5)x.

Determine whether the set of data displays exponential behavior.

Homework

p 427 #11-39 odd, 40