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.”
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.