Getting Started 
Misconception/Error The student is unable to correctly write the exponential function that models the given relationship. 
Examples of Student Work at this Level The student:
 Uses the wrong base and expression for the exponent.
 Makes an error when calculating the base.
 Uses the wrong expression for the exponent.

Questions Eliciting Thinking What is the form of an exponential function? Why can an exponential function model the relationship between the variables?
What are the two important parameters of an exponential function?
What role will the values 100 and 3 play in the equation?
How was the rate of change described? How will that affect the form of the exponent? 
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. Explain what features of the problem indicate that the relationship between the variables can be modeled by an exponential function. Provide opportunities for the student to explore and investigate examples of 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 relate the parameters to the context. Explain to the student that in the included problem, Bacteria Aâ€™s growth rate is given in terms of twohour increments so the exponent can be written as .
Assist the student in writing the function as . If the student attempts to write the exponent as t, explain why the function asÂ Â is an equivalent alternative.
Provide additional opportunities for the student to write exponential functions from verbal descriptions.
If necessary, review function notation. Consider implementing other MFAS tasks for FIF.1.2. 
Moving Forward 
Misconception/Error The student is unable to correctly write the combined function that models the given relationship. 
Examples of Student Work at this Level The student writes the exponential function correctly but:
 Substitutes zero for t and attempts to solve the resulting exponential equation.
 Uses the wrong operation when combining the functions [e.g., writes ].
 Replaces the base in the exponential function with 900, writing .
 Indicates that he or she does not know how to write the combined function.

Questions Eliciting Thinking What are you asked to do in the second problem?
What is happening with Bacteria B? Is it increasing over time? How will it affect the total number of bacteria in the culture?
How many bacteria do you think will be in the culture at the start? After 2 hours? After 4 hours? 
Instructional Implications Review that Bacteria B is nonreproducing and explain how it contributes to the total number of bacteria. Ask the student to revise the equation. Provide additional scenarios concerning Bacteria B (e.g., Bacteria B doubles every hour or increases by 500 every hour) and ask the student to write a function that represents the total number of bacteria in the culture after t hours.
If necessary, review function notation. Consider implementing other MFAS tasks for FIF.1.2. 
Almost There 
Misconception/Error The student is unable to use the function to solve for t when given a number of bacteria. 
Examples of Student Work at this Level The student correctly writes each function but is unable to use the combined function to solve for t to determine when the number of bacteria in the culture will reach 9000.

Questions Eliciting Thinking How did you attempt to calculate the length of time it will take for the bacteria to reach 9000?
I see that you substituted 9000 for the dependent variable. Where did you begin to have trouble when you attempted to solve? 
Instructional Implications Show the student how to use his or her equation to determine when the total number of bacteria will reach 9000. Model rewriting Â as Â and explain that if the bases are the same, the exponents must be equal. Guide the student to write the equation Â and solve.
Provide additional opportunities to solve simple exponential equations.
If necessary, review function notation. Consider implementing other MFAS tasks for FIF.1.2. 
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 exponential function as . The student states that B(t) = 900 so that . To determine when the number of bacteria reaches 9000, the student writes the equation Â and correctly solves for t and concludes that it will take 8 hours for the bacteria to number 9000.

Questions Eliciting Thinking What do you think the graph of the exponential function looks like?
Is B(t) = 900 a function? What will its graph look like?
How will the graph of the exponential function compare to the graph of the combined functions? 
Instructional Implications Introduce composition of functions. Consider implementing MFAS task Furniture Purchase (FBF.1.1). 