Montana Math MT.CORE.ALG.EXP.2

MathGrades 9–12Exponential Functions and Expressions

The Standard

Understand a as the initial value and b as the growth/decay factor for an exponential function written in standard form, y = a · b^x.

2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning

Teacher's field guide

What Students Need to Do: Students identify the starting value and the multiplier in an exponential equation. They use the multiplier to tell whether values grow or shrink, then find values at later steps.
What Mastery Looks Like: For y = 120(0.8)^x, a student says the value starts at 120 and drops 20% each step. They calculate 96 at x = 1 and 76.8 at x = 2.
Common Misconceptions: Students may treat the starting value as the value at x = 1 instead of x = 0. They may read 0.8 as an 80% drop, or subtract 0.8 each step instead of multiplying by it.
How to Assess It: Exit ticket: A bike's value is V = 80(0.75)^t, where t is years. What is its starting value, yearly percent change, and value after two years?

Lesson moves

Give groups 40 counters; have them remove half each round, record counts for rounds 0 through 3, and write the matching equation.
Put y = 50(1.2)^x and y = 50 + 1.2x on the board; ask which multiplies each step and how they know.
Have pairs match equation cards y = 30(1.5)^x and y = 90(0.5)^x to table cards showing 30, 45, 67.5 and 90, 45, 22.5.
Give students a $600 phone resale listing with a 20% yearly value drop; ask for the model and next year's value.

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