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