Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.6: Optimization
Problem 24E
Related questions
Question
Transcribed Image Text:Profit
(thousands of dollars)
O Carnegie Learning, Inc.
ACTIVITY
5.2
Average Rate of Change
and not $600 per year.
dependent variable to the change in the independent variable over
specific interval. The formula for average rate of change is
interval (a, b). The expressionb-a represents the change in the innu
values of the function f The expression f(b) - (a) represents the cha
the output values of the function fas the input values change from oe
Ab) – la)
b-a
for the
Explain why the average rate of change is positive over this
interval.
sk
O yourself:
- What does the average rate of change represent in this
what other
Worked Example
problem situation?
You can determine the average rate of change of Zorzansa's profit for
the time interval (3.25, 4.25).
cion types have
previously
mined the
ge rate of
ge? Is the formula
Zorzansa's Profits Over
Years 0-5
2. Determine the average rate of change of Zorzansa's profits for
the time interval (1, 3).
ame?
p(x) 4
800
-278
279
400
3. Sam has a theory about the average rate of change. Describe
the error in Sam's reasoning.
-400-
-800
Sam
I can quickly estimate the average vate of change for intervals that are above
and below the x-axis because they add to zero. For example, at year I, the profit
is about $300,000 and at year 2.25 the profit is about -$300,000. Therefore, the
average vate of change for the time interval (1, 2.25) is approximately $0.
Time (years)
Substitute the input and output values
into the average rate of change formula.
fib) – fla)_ f(4.25) – f(3.25)
b-a
4.25 - 3.25
Evaluate the expression.
0- (-600)
600
= 600
The average rate of change for the time interval (3.25, 4.25) is
approximately $600,000 per year.
1. example.
The of of a function is the ratio of the change in the
LESSON 5: Level
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