Getting Started 
Misconception/Error The student does not understand the basic form of an exponential function. 
Examples of Student Work at this Level The student:
 Writes an expression involving an exponent.
 Writes a linear equation.

Questions Eliciting Thinking What is an exponential function?
What does the equation of an exponential equation look like? 
Instructional Implications 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, as well as the basic form of an exponential function, y =Â . 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. 
Moving Forward 
Misconception/Error The student is unable to correctly calculate one or both parameters. 
Examples of Student Work at this Level The student:
 Writes the compound interest formula but calculates neither parameter of the function.
 Errs in calculating the growth factor (e.g., writing it as 0.05 instead of 1.05).

Questions Eliciting Thinking What can this formula be used to calculate? Can it be applied to this problem?
What does the amount 650(0.05) represent in this problem?
What are the two important parameters of an exponential function? Can you describe them in words? 
Instructional Implications Review the basic form of an exponential function, y = , and the meaning of the two parameters, a (the initial amount) and b (the growth/decay factor). Ask the student to make a table of values for the problem in this task that contains a column for t (from t = 0 to t = 5), a column that shows the calculation of corresponding values of V [e.g., for t = 1: 650 + 0.05(650)], and a column for the calculated value of VÂ (e.g., 682.50). Guide the student to see the relationship between 650 + 0.05(650) and 1.05(650). Make sure the student understands that the growth factor is (1 + r) where r is the rate of growth. Provide an example of exponential decay and use it to explain that the decay factor is of the form (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. 
Almost There 
Misconception/Error The student does not completely simplify the equation or provides an inadequate explanation. 
Examples of Student Work at this Level The student:
 Correctly uses the compound interest formula to write the function but neglects to completely simplify (by substituting one for n).
 Does not simplify (1 + 0.05) and fails to provide an adequate explanation.
 Neglects to include the exponent (t) in the final version of the equation.

Questions Eliciting Thinking What is the 650 in this problem? What is the .05?
Why did you write your equation this way? Can you explain to me the parts of your equation? 
Instructional Implications Provide specific feedback to the student and allow the student to revise the function or explanation. Model explaining why the function is written as V = using appropriate mathematical terminology.
Provide additional opportunities for the student to write exponential functions from verbal descriptions, tables of values, and graphs. 
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 V = and explains that 650 is the initial value of the desk and 1.05 is the growth factor since the rate of appreciation in the value is 5% or 0.05.

Questions Eliciting Thinking If the value of the desk was increasing by 5% each quarter, how would your function change?
How would the function change if the desk were depreciating or losing value every year? 
Instructional Implications Ask the student to compare linear functions to exponential functions and distinguish between problem contexts that can be modeled by each. Be sure the student understands that linear growth occurs at a constant rate while exponential growth is characterized by a common ratio. Provide descriptions of variables that are related either exponentially or linearly and challenge the student to determine which function best models the relationship between the variables.
Consider implementing other MFAS exponential tasks Writing an Exponential Function From a Graph (FLE.1.2), Writing an Exponential Function From a Table (FLE.1.2), and What Is the Function Rule? (FLE.1.2). 