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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
Answers
3.352 × 106
2.81 × 10–6
30,000
0.0000612
3 × 108
Exponential Functions
Lesson 7-5
Understand how to graph exponential
functions and to identify data that
display exponential behavior.
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 of
x 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.
B. Use the graph of y = 5x to
determine the approximate value
of 50.25.
Graph with a > 0 and 0 < b < 1
A.
Find the y-intercept and state
the domain and range.
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.
Graph with a > 0 and 0 < b < 1
Answer: The value of y is about
8 when x = –1.5.
Use a calculator to confirm
this value.
A. Graph
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?
A. $21,000
B. $23,600
C. $18,040
D. $20,000
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
× 2.5
× 2.5
62.5
× 2.5
156.25
Identify 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.
Method 2 Graph the data.
Answer: The graph shows
rapidly increasing
values of y as x
increases. This is
a characteristic of
exponential behavior.
Determine whether the set of data displays
exponential behavior.
Homework
Page 427 #11-39 odd,
26, 40,
51-67 odd