Unit 06 · 3 Weeks · 7 Lessons
Exponential Functions & Growth Models
How do repeated multiplication, percent change, and continuous growth create exponential patterns and decisions?
Complete instructional sequence
Detailed Lessons
Lessons include objectives, formulas, concept development, worked examples, guided and independent practice, differentiated pathways, application, misconception analysis, mastery evidence, reflection, and local completion.
Exponential Function Structure & Parameters
The initial value a and growth factor b determine an exponential function. Equal input increases multiply outputs by a constant factor rather than adding a constant difference.
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Lesson 02Growth, Decay & Percent Change
Discrete exponential change uses a per-period multiplier. Growth uses 1+r; decay uses 1−r. Time units must match the stated rate period.
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Lesson 03Compound Interest & Effective Rates
Compound interest depends on principal, nominal annual rate, compounding frequency, and time. Effective annual rate allows fair comparisons.
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Lesson 04Continuous Growth, Decay & the Constant e
Continuous growth and decay use the natural base e. The sign and units of r determine direction and time scale.
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Lesson 05Solving Exponential Equations by Common Bases
If exponential expressions can be expressed with the same base, equate exponents. Otherwise logarithms are required later.
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Lesson 06Exponential Regression & Data Modelling
Exponential regression estimates multiplicative change from data. A strong fit requires more than a coefficient: inspect residuals, domain, mechanism, and uncertainty.
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Lesson 07Comparing Linear, Quadratic & Exponential Models
Linear models have constant differences, exponential models have constant ratios, and quadratic models have constant second differences. Model choice should be evidence-based.
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Practice and evidence
Unit Resources
Foundation Practice
Prerequisite support, smaller steps, representation aids, and correction prompts.
Core Practice
Complete standards-level definitive-answer practice and explanation.
Extended Practice
Generalization, proof, parameter analysis, technology, and deeper modelling.
Unit Mastery Check
Fresh randomized questions with scoring and explanations.
Exponential Growth, Decay & Financial Scenario Audit
Applied investigation with evidence, validation, limitations, and defense.
Family Guide
Plain-language overview, support questions, and evidence expectations.
Teacher Guide
Pacing, differentiation, assessment, misconceptions, and records.
Vocabulary Data
Core English terms with Spanish, French, Arabic, and Portuguese support.
Standards Map
Unit concepts and broad national/international alignment categories.