Getting Started 
Misconception/Error The student does not indicate an understanding of the given exponential expression. 
Examples of Student Work at this Level The student rewrites the expression in a nonequivalent form:
 Without regard to the exponent.
 By attempting to manipulate both the base and the exponent.
 By writing the expression as or but without demonstrating an understanding of the meaning of .

Questions Eliciting Thinking In the given function , what does t represent? What does P represent? What is the meaning of the base, 1.03?
Suppose you substituted 10 for t and calculated . What is the significance of this value? 
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, . 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.
Remind the student that 1.03 is the growth factor, and the rate of growth is 0.03 or 3% annually. Explain to the student that represents the percent increase after one decade. Ask the student to write expressions to represent the percent increase after two decades (i.e., ), three decades (i.e., ), and four decades (i.e., ). Guide the student to rewrite each exponent in the form 10T where T is a number of decades (e.g., 10 = 10*1; 20 = 10*2; 30 = 10*3; and 40 = 10*4) and to observe that, in general, t = 10T. Guide the student to rewrite the expression as .
Provide additional opportunities to rewrite exponential expressions in equivalent forms in both realworld and mathematical problems. 
Moving Forward 
Misconception/Error The student demonstrates some understanding of the meaning of the given exponential expression but is unable to rewrite the expression to represent the percent increase per decade. 
Examples of Student Work at this Level The student calculates the percent increase for one decade and interprets this value correctly. However, the student does not rewrite the original expression in an equivalent form to represent the percent increase each decade.

Questions Eliciting Thinking What does or 1.34 represent in the context of this function?
How would you use this expression to calculate the percent increase each decade?
Can you write an expression in terms of T, the number of decades? 
Instructional Implications Remind the student that the (1.03) in this equation is the growth factor, and the rate of growth is 0.03 or 3% annually. Explain to the student that represents the percent increase after one decade. Ask the student to write expressions to represent the percent increase after two decades , three decades , and four decades . Guide the student to rewrite each exponent in the form 10T where T is a number of decades (e.g., ) and to observe that, in general, t = 10T . Guide the student to rewrite the expression as .
Provide additional opportunities to rewrite exponential expressions in equivalent forms in both realworld and mathematical problems. 
Almost There 
Misconception/Error The student errs in showing work or is unclear about the meaning of the variable representing time. 
Examples of Student Work at this Level The student writes:
 but is unable to clearly identify the meaning of d.Â

Questions Eliciting Thinking Is = = ?
What does t represent in your expression â€“ time in years or time in decades? 
Instructional Implications Model how to rewrite the expression in an equivalent form, so the variable representing time is measured in decades: where T represents number of decades. Emphasize the meaning of the variable, t, in the original expression and the meaning of the variable, T, in the new expression. Ask the student to evaluate the original expression for t = 20 and the new expression for T = 2 to confirm that they result in the same value of P (taking into consideration that ). Challenge the student to use properties of exponents to show that by considering the meaning of the variables t and T.
Provide additional opportunities to rewrite exponential expressions in equivalent forms in both realworld and mathematical problems. 
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 uses properties of exponents to transform the original expression, so it can be used to calculate the percent increase in the cost of college tuition each decade. The student writes:
 where t represents number of years, or
 where T represents number of decades.Â

Questions Eliciting Thinking What is the percent increase in the cost of tuition per decade? 
Instructional Implications Challenge the student to use properties of exponents to show that by considering the meaning of the variables t and T.
Provide additional opportunities to rewrite exponential expressions in equivalent forms in both realworld and mathematical problems.
Consider implementing MFAS tasks Jumping Dolphin (ASSE.2.3), Rocket Town (ASSE.2.3) and Population Drop (ASSE.2.3). 