All students should graduate from high school ready for college, careers, and citizenship.

**1. Understanding**

The student is correctly using the units and parameters to calculate the amount of time it would take to fill the pool in question 2.

**1. Understanding**

The student clearly distinguishes between discrete and continuous graphs in the exponential situations, but not in the linear situations.

**2. CCSS Alignment**

The student distinguishes between situations that can be modeled as linear functions and those that can be modeled as exponential functions.

**Standard referenced:**

**HSF-LE.A.1: **Distinguish between situations that can be modeled with linear functions and with exponential functions.

**3. CCSS Alignment**

The student can construct linear and exponential functions with both explicit and recursive representations. The student does not include the initial value f(0) in the equation, but instead used the term at f(1), and adjusts the equation accordingly.

**Standard referenced:**

**HSF-LE.A.2: **Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

**4. Comprehension & Application**

**SMP.7**: Look for and make use of structure.

The student displays very clear structure in each of the explicit and recursive equations, even adjusting the parameters in the explicit equation to reflect the use of the amount present when x = 1. The additional calculations in the work suggest that the student is using the structure of the function type as a tool to facilitate reasoning.

**CCSS Alignment**

**(Entire page)**

There is evidence that the student has a depth of understanding for how to create linear and exponential functions, and fluency in working with large numbers and looking at units to help facilitate the writing of the equations.

**Standard referenced:**

**HSF-LE.A.2: **Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

**1. CCSS Alignment**

The student understands that the percent growth factor represents exponential growth. There is evidence that this observation was made while creating the table. The student is drawing upon the student’s understanding of geometric sequences to make the conclusion that the exponential function will continue to grow by larger numbers over time.

**Standard referenced:**

**HSF-LE.A.1c: **Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

**2. CCSS Alignment**

The student is able to understand the parameters correctly in both the recursive and explicit equations for both types of functions.

**Standard referenced:**

**HSF-LE.B.5: **Interpret the parameters in a linear or exponential function in terms of a context.

**3. Understanding**

Because the student has an understanding of how linear functions grow compared to how exponential functions grow, the student was able to predict that the exponential function would overtake the linear function, and recognized that there was only one point of intersection.

**1. Comprehension & Application**

**SMP.7**: Look for and make use of structure.

The student uses the graph first to predict, and then by including additional points, refine the student’s prediction. The original graph was scaled in a way that was difficult to see the features of the exponential function, so the student adjusted the scale of the graph in order to make a better comparison.

**2. CCSS Alignment**

Evidence that the student has mastered HSF-LE.A.3 can be found in the student’s graph and written work. The student is able to use the graph to make a prediction by sketching what the graph could look like, and then continues to use the graph to test that prediction in a more precise way. The student has written an equation, which, if it could be solved, would determine the point of intersection. The student notices that the lines will only intersect once for this context, by writing, “They will never have the same net value again.”

**Standard referenced:**

**HSF-LE.A.3: **Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.