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BetterGrades Algebra · Unit A13 · Unit Hub

Unit A13: Exponential and Logarithmic Algebra

Complete the Algebra course with repeated proportional change, inverse exponentiation, and equation solving. How do we describe multiplicative change and solve for an unknown exponent?

Act XIII - Describing multiplicative change and undoing it

The 11-lesson path

Constant differences are contrasted with constant ratios. Repeated percentages produce exponential models, compounding motivates e, and logarithms reverse exponentiation. Log laws follow from exponent laws and solve previously inaccessible equations.

Governing question

How do we describe multiplicative change and solve for an unknown exponent?

Complete the Algebra course with repeated proportional change, inverse exponentiation, and equation solving.

Mastery design

Know when to continue

Students construct models, solve exact and approximate equations, and reject logarithmic candidates outside the domain.

Unit outcomes
  1. Distinguish additive from multiplicative patterns.
  2. Construct and interpret exponential growth and decay models.
  3. Use compound and continuous growth formulas.
  4. Define logarithms as inverse exponentiation and use log laws.
  5. Solve exponential and logarithmic equations with domain checks.
Core sequence

Lessons

Move in order when this material is new; use prerequisites and repair links when entering mid-unit.

  1. 01Additive versus multiplicative patternsDistinguish constant difference from constant ratio in tables, graphs, and contexts.
  2. 02Geometric sequences and repeated percent changeWrite repeated multiplication as an explicit geometric rule.
  3. 03Exponential functionsInterpret f(x)=abx,f(x)=ab^x, parameter restrictions, initial value, and growth or decay.
  4. 04Graphs and transformations of exponentialsRead simple shifts and scales and track the horizontal asymptote.
  5. 05Growth and decay modelsBuild a model from initial value and percentage rate and interpret its valid domain.
  6. 06Compound interestCompare compounding periods and calculate accumulated balance.
  7. 07Continuous growth and eMotivate ee through increasingly frequent compounding and use continuous growthdecay\frac{growth}{decay} models.
  8. 08Logarithms as inverse operationsInterpret log_b(y) as the exponent producing yy and state baseargument\frac{base}{argument} restrictions.
  9. 09Logarithm lawsDerive product, quotient, and power laws from exponent laws and reject false sum rules.
  10. 10Solving exponential equationsUse common bases or logarithms and preserve exact form before decimal approximation.
  11. 11Solving logarithmic equations and logarithmic modelsCondense, exponentiate, and reject candidates with invalid log arguments.

Practice around the path

Review, mixed practice, mastery, and investigation

Every route contains a fixed set of concrete questions, with detailed solutions available after an attempt.

ReviewCumulative reviewRevisit this unit with prior-unit retrieval.PracticeMixed practiceClassify the structure before choosing a method.MasteryMastery checkUse the supplied grading and cumulative-share contract.InvestigationPerformance taskCompare linear, exponential, and logarithmic claims made from the same data and decide which conclusions are justified.Response guideMastery response guideAttempt-gated rubric support; no invented canonical answers.

Source & rights

Original storyboard, rights-separated references.

Public page content comes from the BetterGrades Algebra editorial storyboard supplied by the owner. Reference books named in provenance remain separate and are not copied into the application.