Free Printable WorksheetMathPre-CalculusMath CurriculumHSF-LE.1-5

Pre CAL.64 Fitting Exponential and Logarithmic Models Using Technology Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Pre-Calculus Math worksheet provides structured practice on Pre CAL.64 Fitting Exponential and Logarithmic Models Using Technology. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.64 Fitting Exponential and Logarithmic Models Using Technology - Primary standard selected for prompt fields in this prompt cell: CCSS HSF-LE.1-5. Skill statement in this prompt cell: Given regression output and data, select the correct exponential or logarithmic model and determine which model is most reasonable based on residuals and context. Associated standards listed with this skill in this prompt cell: CCSS HSF-LE.1-5; CCSS HSF-BF.3-5(+); CCSS HSA-REI.11; SMP 1,2,4,5,7; AP Precalculus CED Unit 2; TX §111.42(c)(5)(J-M); FL MA.912.AR.5; VA MA.FR.2. 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

Pre-Calculus

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 Pre CAL.64 Fitting Exponential and Logarithmic Models Using Technology skill assessments:

Problem 1Difficulty: Mastery
Use the model comparison visuals shown for the same data. The exponential fit's residuals curve upward at high x, while the logarithmic fit's residuals are small and random. Which model should be selected?
ALogarithmic, because its residuals are small and unpatterned
BExponential, because all residual curves are acceptable
CExponential, because the variable x is positive
DNeither, because residual plots cannot compare models
Solution & Explanation:The logarithmic model leaves less systematic error. Small random residuals are stronger evidence than a curved residual pattern.
Problem 2Difficulty: Mastery
A selected exponential model is y = 4.2(1.35)x. At x = 6, the actual value is 26.9. What is the residual actual - predicted, rounded to the nearest tenth?
Solution & Explanation:The prediction is 4.2(1.35)6 = 25.4 to the nearest tenth. The residual is 26.9 - 25.4 = 1.5 to the nearest tenth.
Problem 3Difficulty: Mastery
Data and output show: Exponential y = 3.7(1.41)x, R2 = 0.984, residuals increase from negative to positive; Logarithmic y = 9.8 + 6.1ln(x), R2 = 0.981, residuals random. Which statement is best?
AThe logarithmic model is more reasonable because residuals are random even though R2 is slightly lower
BThe exponential model is better because R2 is slightly larger and residuals do not matter
CBoth models are invalid because R2 is below 1
DThe exponential model is better because negative residuals are impossible
Solution & Explanation:The exponential residuals show a systematic trend. The logarithmic model's random residuals make it the stronger modeling choice despite the tiny R2 difference.

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Pre-Calculus Math students. It aligns with educational standard HSF-LE.1-5 (Primary standard selected for prompt fields in this prompt cell: CCSS HSF-LE.1-5. Skill statement in this prompt cell: Given regression output and data, select the correct exponential or logarithmic model and determine which model is most reasonable based on residuals and context. Associated standards listed with this skill in this prompt cell: CCSS HSF-LE.1-5; CCSS HSF-BF.3-5(+); CCSS HSA-REI.11; SMP 1,2,4,5,7; AP Precalculus CED Unit 2; TX §111.42(c)(5)(J-M); FL MA.912.AR.5; VA MA.FR.2. Use this prompt-provided wording as the supporting standard description for this workflow.).

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