Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 68857
Exponential Functions - 1
Students are asked to identify the percent rate of change of a given exponential function.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, exponential function, exponentials, rate of change, percent rate of change
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_ExponentialFunctions1_Worksheet.docx
MFAS_ExponentialFunctions1_Worksheet.pdf
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be implemented individually, with small groups, or with the whole class.
1. The teacher asks the student to complete the problems on the Exponential Functions - 1 worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student does not understand how to distinguish between exponential growth and decay.
Examples of Student Work at this Level
The student states that the function represents:
Exponential growth because the rate or base is positive or a whole number.
page 1 of 3 Exponential decay because the rate or base is not a whole number.
Questions Eliciting Thinking
What is the form of an exponential function? Why is this function called exponential?
What are the two important parameters of an exponential function?
What does the 50 indicate? What does the 1.1 mean?
Instructional Implications
Review the basic form of an exponential function emphasizing the role of its two parameters: the initial amount and the growth/decay factor. Provide opportunities for the
student to explore and investigate exponential functions, both growth and decay, in context. Have the student make a table of values for each example. Then, guide the
student to identify the two parameters of each function and interpret the parameters in context. Assist the student in understanding why an exponential function is
written in the form
by relating the calculation of the values of y in the table to the form of the function.
Explain the difference between the growth/decay factor and the rate of growth or decay. Explain that the growth factor is (1 + r) where r is the rate of growth and the
decay factor is (1 – r) where r is the rate of decay. Ensure the student understands that r represents the percent rate of change of y with respect to t. Discuss the
relationship between the rate of growth/decay and the growth/decay factor using a specific example of a table of values for an exponential function.
Provide additional opportunities for the student to identify the percent rate of change of an exponential function given its equation.
Making Progress
Misconception/Error
The student does not understand how to determine the percent rate of change.
Examples of Student Work at this Level
The student explains that the function describes exponential growth since the growth factor is greater than one. However, the student is unable to correctly determine
the percent rate of change. The student:
Converts 1.1 to a percent and says the percent rate of change is 110%.
Calculates 1.1(100) ÷ 50 and says the percent rate of change is 2.2%. Multiplies 50 by 1.1 and says the percent rate of change is 55%.
Questions Eliciting Thinking
What happens to the values of y as t increases?
Did you make a table of values to explore the rate of change?
Instructional Implications
page 2 of 3 Explain the difference between the growth/decay factor and the rate of growth or decay. Explain that the growth factor is (1 + r) where r is the rate of growth and the
decay factor is (1 – r) where r is the rate of decay. Ensure the student understands that r represents the percent rate of change of y with respect to t. Discuss the
relationship between the rate of growth/decay and the growth/decay factor using a specific example of a table of values for an exponential function.
Provide additional opportunities for the student to identify the percent rate of change of an exponential function given its equation.
Got It
Misconception/Error
The student provides complete and correct responses to all components of the task.
Examples of Student Work at this Level
The student identifies the function as one describing exponential growth because the base is greater than one (and indicates a growth factor of 110%). To find the
percent rate of change, the student either calculates 1.1 – 1 = 0.1 = 10% or observes that when t increases from zero to one, y increases from 50 to 55. The student
determines that an increase of five from 50 represents a 10% change.
Questions Eliciting Thinking
How can you see from the form of the function that the answer to the second question is 10%?
Would the percent change be greater or less if the base were 1.3 rather than 1.1?
Instructional Implications
Provide the student with an exponential function that represents decay and ask the student to identify the percent rate of change.
Consider implementing the MFAS task Exponential Functions - 2 (F-IF.3.8).
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Exponential Functions - 1 worksheet
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.912.F-IF.3.8:
Description
Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of
the function.
a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and
symmetry of the graph, and interpret these in terms of a context.
b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent
rate of change in functions such as y =
,y=
,y=
,y=
, and classify them as
representing exponential growth or decay.
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