WeSolve+ reads the whole document and writes the questions for you
Upload your PDF, photograph your notebook, or point the camera. WeSolve+ writes questions from that material, explains why each answer is right, reads the chapter back to you as a podcast, and remembers every item you missed until you own it.
The tool below is a small browser-only tool and it is not WeSolve+: paste a few lines and text rules turn them into cards on the spot. The real app, the one that uses AI, is behind the link above.
Unit 2 rules, from your own notes
This is a browser-only tool, and that is all it isIt splits the text you paste by rule, and nothing else. WeSolve+ is a different thing entirely: it reads your whole PDF with AI, writes the reasoning behind every question, speaks the chapter back to you, and remembers what you missed so it can return it. Try the real app now, free!
This tool splits the text you paste by rule and returns cards. It cannot solve an equation or read a table, so it works on the statements you already wrote down.
The test on a table is division, not subtraction
For a linear function, subtracting consecutive outputs gives the same number. For an exponential one, dividing them does. Questions hand you a table and ask which model fits, and running both checks takes ten seconds. Guessing from the shape of the numbers is where students lose an easy mark.
The logarithm is an inverse, and thinking of it that way removes the fear
It answers one question: what exponent produces this value from this base. Every logarithm rule follows from an exponent rule read backwards, so learning the two sets separately doubles the work for no benefit. Write the exponential form beside the logarithmic one until the translation is automatic.
Logs turn multiplication into addition, which is the point
That property is why they were invented and why they appear wherever quantities span many orders of magnitude. When a question involves a product inside a logarithm, splitting it is almost always the intended first move, and recognising that saves more time than any algebraic shortcut in this unit.
Asymptotes swap when you take the inverse
An exponential graph approaches a horizontal line; its inverse approaches a vertical one. That is not two facts to memorise but one fact seen from two sides, because reflecting a graph in the diagonal exchanges horizontal and vertical. Noticing that connection is exactly the reasoning this course rewards.
Doubling time and half life are the same statement
Both say that a fixed multiplier applies over a fixed interval, one greater than one and one less. Half life problems and compound growth problems therefore use identical machinery, and students who treat decay as a separate topic end up learning the same method twice.
What to photograph for Exponential and Logarithmic Functions
Your worked examples, including the wrong ones with the correction beside them. Related: Unit 1, photo to quiz and pricing.
Sources used on this page
- College Board, AP Precalculus
- Exponential function
- Logarithm
- Exponential growth
- Half-life
- Active recall
- Spaced repetition
- Testing effect
- Forgetting curve
- Generation effect
- Judgment of learning
- Metacognition
- Desirable difficulty
- Distributed practice
- Formative assessment
- Flashcard
- Cloze test
- Multiple choice
- Test (assessment)
- Educational assessment
- Advanced Placement
- Curriculum
- Study skills
- Study guide
- Note-taking
- Overlearning
- Instructional scaffolding
- Item analysis
- Mastery learning
| Check | Linear | Exponential |
|---|---|---|
| Consecutive outputs | Constant difference | Constant ratio |
| Test on a table | Subtract | Divide |
| Graph | Straight line | Horizontal asymptote |
| Inverse | Another line | Logarithm |
| Doubling | Takes longer each time | Takes the same time always |
| Typical wording | Increases by an amount | Increases by a percentage |
What is AP Precalculus Unit 2?
Exponential and Logarithmic Functions: growth by constant ratio, the logarithm as an inverse, and the graphs and applications of both.
How do I tell exponential from linear in a table?
Subtract consecutive outputs for linear and divide them for exponential. Whichever gives a constant number is the model that fits.
What is a logarithm, in one sentence?
The operation that returns the exponent needed to produce a given value from a fixed base. Every log rule is an exponent rule read backwards.
Why do logs turn products into sums?
Because exponents add when powers are multiplied. That property is why logarithms were invented and why splitting a product is usually the intended first move.
Why do the asymptotes swap for the inverse?
Because reflecting a graph in the diagonal exchanges horizontal and vertical. It is one fact seen from two sides rather than two facts.
Are decay problems different from growth problems?
No. Half life and doubling time both state a fixed multiplier over a fixed interval, so the machinery is identical.
Last updated: 2026-08-15