This lesson asks students to find the value of an exponent in an exponential expression or equation. Its purpose is to motivate the need to “undo” exponentiation and prepare students for the upcoming work on logarithms.
Students encounter two situations characterized by exponential growth—one discrete and one continuous. They write and evaluate exponential expressions to solve problems about these situations. Along the way, they come across problems that require finding the exponent in an exponential expression. Students notice that they can do so by reasoning, estimating, or using other strategies, but the process is often not straightforward and is not as simple as solving for a variable in other equations they have seen so far. Solving for an unknown exponent, especially when it is not an integer, requires students to make sense of the quantities in a situation and persevere in their reasoning or estimation (MP1).
The lesson also includes an optional activity that prompts students to think about solving for an exponent but without context.
Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.
Lesson overview
 8.1 Warmup: A Bunch of \(x\)’s (5 minutes)
 8.2 Activity: A Tessellated Trapezoid (15 minutes)

8.3 Activity: Successive Splitting (15 minutes)
 Includes "Are you Ready for More?" extension problem
 8.4 Optional Activity: Missing Values (10 minutes)
 Lesson Synthesis
 8.5 Cooldown: Video Viewers (5 minutes)
Learning goals:
 Comprehend the need to "undo" exponentiation to solve problems in simple contexts.
 Explain (orally and in writing) how to determine the value of an unknown exponent both exactly and approximately.
Learning goals (student facing):
 Let’s find unknown exponents.
Learning targets (student facing):
 I can approximate the value of unknown exponents.
Required materials:
 Scientific calculators
Standards:
 This lesson builds on the standards: CCSS.HSAREI.B.4.bMS.AREI.4bMO.A1.REI.A.2cCCSS.HSFLE.A.2MS.FLE.2MO.A1.LQE.A.3
 This lesson builds towards the standard: CCSS.HSFLE.A.4MS.FLE.4MO.A2.SSE.A.2MO.A2.SSE.A.3MO.A2.SSE.A.1
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