In this lesson, students examine the meaning of negative exponents in context. In these situations, a value of  that is less than 0 corresponds to a time before the initial measurement, while a value of that is greater than 0 refers to a time after the measurement. Students write equations given a table, and then use those equations to answer questions, which requires working with negative values representing time. In one case, students also produce a graph. As with many other activities in this unit, the mathematical work is grounded and interpreted in a context (MP2).

An optional activity here addresses the difficulties inherent in producing graphs representing exponential change, namely that the graphing window has to be selected carefully in order for the graph to be useful. The savvy setting of a graphing window is an important skill when using graphing technology, and intentionally addressing this skill puts students in a better position to use technology strategically in the future.