Getting Started 
Misconception/Error The student is unable to correctly write a function that models the given relationship. 
Examples of Student Work at this Level The student:
 Does not attempt to write a function.
 Writes a linear function such as M(n) = 1,000,000 â€“ 2n.
 Answers the question using a recursive process.

Questions Eliciting Thinking Can you restate the situation described in the problem?
What are you being asked to find? What information are you given?
How would you describe what is happening to the prize amount each day? 
Instructional Implications Assist the student in first identifying the relevant variables and quantities in the problem description and then verbally describing their relationship. Guide the student to translate the verbal description into an equation using the notation given in the problem. Show the student how to use the equation to calculate the amount won on the 15th day. Help the student identity the starting amount growth factor. Model using function notation appropriately.
Review the basic form of an exponential function. 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. Encourage the student to observe not only a recursive relationship but also the explicit relationship between the inputs and outputs. Then guide the student to identify the two parameters of an exponential function (the initial amount and the growth/decay factor) and write the equation. Be sure the student understands 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 â€“ r) where r is the rate of decay. Provide additional opportunities for the student to write exponential functions from verbal descriptions, tables of values, and graphs.
If necessary, review function notation. Consider implementing the MFAS task What Is the Function Notation? (FIF.1.2). 
Moving Forward 
Misconception/Error The student attempts to write a function but makes significant errors. 
Examples of Student Work at this Level The student:
 Neglects the starting amount and writes the equation as .
 Confuses the starting amount and the growth factor and writes .
 Makes an error in writing the decay factor and writes the equation as .

Questions Eliciting Thinking Can you explain the problem in your own words? What important information were you given in the problem?
What is the basic form of an exponential function? What are the two important parameters?
By what factor is the amount of prize money changing each day? 
Instructional Implications Review the basic form of an exponential function. 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 an exponential function (the initial amount and the growth/decay factor) and write the equation. Be sure the student understands 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 â€“ r) where r is the rate of decay. Provide additional opportunities for the student to write exponential functions from verbal descriptions, tables of values, and graphs.
If necessary, review function notation. Consider implementing the MFAS task What Is the Function Notation? (FIF.1.2). 
Almost There 
Misconception/Error The student correctly writes a function that models the given relationship but makes a minor error. 
Examples of Student Work at this Level The student:
 Writes the exponent as n when it should be n â€“ 1.
 Does not round according to the constraints of the problem.
 Uses function notation incorrectly or not at all.

Questions Eliciting Thinking I see in your equation that you wrote the exponent as n. Then what is M(1)? Does that match the information given in the problem?
You gave the answer as 30.518. What were you being asked to find? Does this answer make sense?
What is function notation? Which symbol represents the number of days? Which symbol represents the amount of money won? 
Instructional Implications Provide feedback to the student concerning any errors made and allow the student to revise the work.
Review function notation emphasizing the meaning of the symbols n and M(n). Provide explicit feedback to the student concerning any errors in notation that were made and guide the student to correct them. Provide continued opportunities to use function notation. 
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 writes the function in a correct form. For example, the student writes one of the following:
The student correctly calculates and appropriately rounds M(15) as $30.52.

Questions Eliciting Thinking What do you think the graph of this function looks like? How do you know?
Is there any restriction on the domain? Why or why not? 
Instructional Implications Provide the student with opportunities to write equations that define more complex functions and to write equations that define functions when given their graphs. 