Montana Math MT.CORE.ALG.EXP.5

MathGrades 9–12Exponential Functions and Expressions

The Standard

Solve exponential equations graphically, while using technology strategically.

2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning

Teacher's field guide

What Students Need to Do: Students graph each side of an exponential equation as a separate function. They find where the graphs meet and use the x-coordinates as approximate solutions.
What Mastery Looks Like: A student adjusts the graph window to look for more than one crossing. They estimate each x-value and check it in the original equation. They can explain why the x-coordinate, not the y-coordinate, is the solution.
Common Misconceptions: Students may report the y-coordinate of a crossing instead of the x-coordinate. They may miss a crossing because their graph window is too narrow. They may round an approximate answer to an integer without checking it.
How to Assess It: Graph y = 2^x and y = x + 2 with x from -3 to 4. Write both x-values where the graphs meet, then check each in the equation.

Lesson moves

Plot points for y = 2^x and y = x + 2 on graph paper, then use a graphing tool to estimate both crossings.
Ask: At the crossing (2, 4), why is 2 a solution to 2^x = x + 2, but 4 is not?
In pairs, graph 3^x = 12 and 5^x = 20, estimate each solution, and check by substitution.
Graph a $200 savings balance growing 8% yearly and a $300 goal line, then estimate when the balance reaches the goal.

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