Free Printable WorksheetMathAlgebra IIMath CurriculumF-LE.3

ALG2.179 Comparing Exponential and Logarithmic Growth Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.179 Comparing Exponential and Logarithmic Growth. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.179 Comparing Exponential and Logarithmic Growth - Primary standard selected for prompt fields in this prompt cell: CCSS F-LE.3. Skill statement in this prompt cell: Select the correct comparison between how exponential and logarithmic functions change over time and describe long-term behavior using graphs and reasoning. Associated standards listed with this skill in this prompt cell: CCSS F-LE.3; F-IF.7e; CA CCSSM F-LE.3; F-IF.7e; MA 2017 F-LE.3; F-IF.7e; NY NGLS F-LE.3; F-IF.7e; TX TEKS Algebra II: §111.40. Use this prompt-provided wording as the supporting standard description for this workflow.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Algebra II

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related ALG2.179 Comparing Exponential and Logarithmic Growth skill assessments:

Problem 1Difficulty: Mastery
For positive constants A and C and bases b > 1 and d > 1, compare F(x) = C(dx) and G(x) = A log_b(x + 10). Which statement is always true for sufficiently large x?
AF(x) eventually exceeds G(x).
BG(x) eventually exceeds F(x).
CF(x) and G(x) must be equal for all large x.
DBoth functions eventually decrease.
Solution & Explanation:F is positive exponential growth, while G is a shifted and scaled logarithmic function. Exponential growth eventually dominates for sufficiently large x.
Problem 2Difficulty: Mastery
Let 0 < a < 1 and b > 1. Compare f(x) = ax and g(x) = -log_b(x) for large positive x. Which statement is correct?
Af(x) approaches 0 from above, while g(x) decreases without bound, so f(x) is eventually greater.
Bg(x) eventually grows faster because all logarithms increase.
Cf(x) grows without bound because it is exponential.
DBoth functions approach the same negative number.
Solution & Explanation:When 0 < a < 1, ax is exponential decay and approaches 0 from above. Since -log_b(x) goes to negative infinity, f is eventually greater.
Problem 3Difficulty: Mastery
How does a negative coefficient change the long-term behavior of a logarithmic function such as g(x) = -5log_2(x) + 30?
AIt makes g(x) decrease without bound as x grows, so positive exponential growth will eventually be much larger.
BIt makes g(x) grow faster than all positive exponential functions.
CIt removes the vertical asymptote and makes the function linear.
DIt makes g(x) approach 30 from above forever.
Solution & Explanation:As log_2(x) increases without bound, -5log_2(x) decreases without bound. A positive exponential growth function will eventually be far larger.

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Frequently Asked Questions

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Algebra II Math students. It aligns with educational standard F-LE.3 (Primary standard selected for prompt fields in this prompt cell: CCSS F-LE.3. Skill statement in this prompt cell: Select the correct comparison between how exponential and logarithmic functions change over time and describe long-term behavior using graphs and reasoning. Associated standards listed with this skill in this prompt cell: CCSS F-LE.3; F-IF.7e; CA CCSSM F-LE.3; F-IF.7e; MA 2017 F-LE.3; F-IF.7e; NY NGLS F-LE.3; F-IF.7e; TX TEKS Algebra II: §111.40. Use this prompt-provided wording as the supporting standard description for this workflow.).

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