Compare exponential and polynomial growth

Start lessonBegins with Exponential vs linear quadratic · Slides

Teacher tools for this standard

Lesson Plan · Guided Notes · Exit Ticket · Re-teach · Homework

Lesson Plan →Objectives, pacing and practice, built from this lesson's brief.
Guided Notes →One page your students fill in and keep.
Exit Ticket →Three items at the end of class. No student accounts.
Re-teach →After an exit ticket: who missed what, and what to do tomorrow.
Homework →Assign practice; it grades itself.

HSF.LE.A.3

**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.

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.

What you'll learn

Use tables of values to observe that an exponential function eventually produces larger outputs than any linear function, regardless of the linear function's slope
Use tables of values to observe that an exponential function eventually produces larger outputs than any quadratic (or higher-degree polynomial) function
Identify the crossover point where an exponential function overtakes a polynomial function by comparing values in a table or on a graph
Explain in plain language why exponential growth dominates: multiplicative growth compounds while additive (or polynomial) growth does not
Interpret graphs that show exponential and polynomial functions together, identifying regions where one exceeds the other
Apply the dominance principle to real-world contexts (e.g., why compound interest eventually outpaces any fixed salary increase)

Review first: