CCSSAPhigh school
AP Precalculus -- Exponential and Logarithmic Functions
Master exponential and logarithmic functions for the AP Precalculus exam. You will connect sequences to functions, model real-world growth and decay, wield logarithm properties to solve equations, and use semi-log plots to validate your models -- all skills tested in Units 2-3.
5units
8topics
139questions
~3hours
Course Units
Learning objectives
- Write explicit and recursive formulas for arithmetic sequences and identify the common difference
- Write explicit and recursive formulas for geometric sequences and identify the common ratio
- Distinguish arithmetic (additive) from geometric (multiplicative) patterns in tables and contexts
- Connect arithmetic sequences to linear functions and geometric sequences to exponential functions
- Determine the nth term of a sequence from a real-world context
Topics in this unit
Learning objectives
- Identify exponential growth (b > 1) and decay (0 < b < 1) from equations and graphs
- Apply transformations (shifts, reflections, stretches) to exponential functions and describe their effects
- Model real-world phenomena with exponential functions (population, radioactive decay, compound interest)
- Determine the growth/decay rate and initial value from a function or data set
- Convert between different exponential forms including base-e and arbitrary-base representations
Topics in this unit
Learning objectives
- Convert between exponential and logarithmic forms fluently
- Apply properties of logarithms (product, quotient, power rules) to expand and condense expressions
- Graph logarithmic functions and identify domain, range, vertical asymptote, and key points
- Recognize logarithms as inverses of exponential functions and use this to solve problems
- Evaluate logarithms of any base using the change-of-base formula
Topics in this unit
Learning objectives
- Solve exponential equations by taking logarithms of both sides and isolating the variable
- Solve logarithmic equations by converting to exponential form
- Identify and check for extraneous solutions that arise from domain restrictions
- Apply these techniques to real-world problems (half-life, doubling time, pH, decibels)
- Solve equations involving multiple exponential or logarithmic terms
Topics in this unit
Learning objectives
- Interpret semi-log plots and explain why exponential data appears linear on them
- Use residual analysis to evaluate how well a model fits the data
- Compare linear, exponential, and polynomial models for a given dataset and justify your choice
- Transform data using logarithms to achieve linearity and extract model parameters
- Identify when a dataset does not follow an exponential trend from semi-log plot curvature
Topics in this unit