College Algebra Modeling
A free College Algebra lesson from the “Modeling and Readiness” unit, with a worked example and practice problems including step-by-step solutions.
Modeling means choosing a function type that matches a situation. Linear models use constant difference, exponential models use constant percent change, and quadratics model many maximum or minimum contexts.
What you'll learn
- Choose function families
- Interpret parameters
- Compare model behavior
Worked example
Problem. A value starts at 400 and grows by 6% each year. What model family fits?
- The starting amount is fixed.
- The change is a constant percent.
- Constant percent change points to exponential growth.
Answer: exponential growth
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (multiple choice and typed response). Counts include repeated prompts and variants.
Practice problems
1. A plan charges a fixed fee plus dollars per month. Which model fits?
Choices: Linear · Quadratic · Exponential · Circle
Show solution
- The amount changes by a constant amount.
Answer: Linear
2. A population grows by 3% each year. Which model fits?
Choices: Exponential · Linear · Quadratic · Absolute value
Show solution
- Constant percent change.
Answer: Exponential
3. A value starts at 250 and decays by 20%. What multiplier is used?
Show solution
- 1 - 0.20 = 0.80.
Answer: 0.8
4. Outputs 10, 15, 20, 25 have a constant difference. Which model fits?
Choices: Linear · Exponential · Quadratic · Logarithmic
Show solution
- Constant difference suggests linear.
Answer: Linear
5. Outputs 3, 6, 12, 24 have a constant ratio. Which model fits?
Choices: Exponential · Linear · Quadratic · Absolute value
Show solution
- Constant ratio suggests exponential.
Answer: Exponential
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