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BetterGrades Precalculus · Unit 7 · Unit map

Exponential and Logarithmic Functions

Constant first differences indicate additive linear change; constant ratios indicate multiplicative exponential change.

Precalculus · Unit 7

The lesson path

Constant first differences indicate additive linear change; constant ratios indicate multiplicative exponential change.

Core sequence

Exponential and Logarithmic Functions

Move in order when the material is new, or enter at the exact skill you need.

  1. 01Additive versus multiplicative changeDistinguish linear, exponential, and neither patterns by comparing equal-input differences, ratios, and percent changes.
  2. 02Exponential functions and parametersAnalyze f(x)=abxf(x)=ab^x by interpreting initial value, base, multiplier, percent rate, domain, range, and asymptote.
  3. 03Exponential transformationsAnalyze transformed exponential functions and track asymptotes, domain, range, and feature points.
  4. 04Growth and decay modelsConstruct exponential models from an initial value, rate, multiplier, two points, or a known doubling or half-life.
  5. 05Compound interest and effective rateUse periodic compounding models and compare nominal rates, periodic rates, compounding frequency, and effective annual yield.
  6. 06Continuous growth and the number eUse A(t)=A0e(kt)A(t)=A0e^(kt) for continuous proportional change and interpret the continuous rate parameter kk.
  7. 07Exponential regression and residualsFit an exponential model to data, interpret parameters, inspect residuals, and evaluate interpolation and extrapolation.
  8. 08Logistic and bounded growthAnalyze logistic growth qualitatively and interpret initial value, carrying capacity, growth rate, and inflection behavior.
  9. 09Logarithms as inverse functionsDefine log base bb as the inverse of bx,b^x, convert between forms, and interpret logarithms as exponents.
  10. 10Logarithmic graphs and transformationsAnalyze transformed logarithmic functions, including domain, range, vertical asymptote, intercepts, and base-dependent direction.
  11. 11Logarithm lawsDerive and apply product, quotient, and power laws while preserving positive-argument domains.
  12. 12Solving exponential equationsSolve exponential equations using common bases, logarithms, and numerical methods, and interpret exact and approximate answers.
  13. 13Solving logarithmic equations and interpreting inverse modelsSolve logarithmic equations, reject invalid arguments, and use logarithms to analyze doubling time, half-life, and logarithmic scales.
Source record

References used for this unit

  • Yoshiwara, Modeling, Functions, and Graphs
  • Lippman and Rasmussen, Precalculus Volume 1
  • Stitz and Zeager, Precalculus

The learner copy is original BetterGrades material informed by these rights-separated references; no long source passage is reproduced.