In this lesson, students rewrite exponential equations and expressions by converting the units of the input from one time period to another. For example, given a description of population growth over decades, write an equation for the population that describes the annual growth.

Students are introduced to the scientific term half-life as the time it takes for half of a certain material to decay into another type of material. They use this context to write an exponential function with a growth factor of and an input of the number of half-life time intervals that have passed, then consider how to rewrite the function using smaller time intervals.

Students must reason abstractly and quantitatively to understand expressions in context (MP2), attend to the precision of the units used for the inputs (MP6), and construct viable arguments for how the growth factor changes in equal subintervals (MP3).