Modeling with Functions
A free Algebra II lesson from the “Trigonometry and Modeling” unit, with a worked example and practice problems including step-by-step solutions.
Modeling means choosing a function family that matches a situation. Linear models have constant change, quadratic models have turning points, and exponential models have constant percent change.
What you'll learn
- Choose function families for contexts
- Interpret parameters
- Compare models
Worked example
Problem. A population starts at 500 and grows by 8% each year. Which model fits?
- The starting amount is 500.
- Growth by 8% is constant percent change.
- Constant percent change points to an exponential model.
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 taxi fare increases by the same dollar amount per mile. Which model fits?
Choices: Linear · Quadratic · Exponential · Trigonometric
Show solution
- Constant rate of change.
Answer: Linear
2. A ball's height rises and then falls. Which model often fits?
Choices: Quadratic · Linear · Exponential · Rational only
Show solution
- Projectile height is often quadratic.
Answer: Quadratic
3. A bank account grows by 4% each year. Which model fits?
Choices: Exponential · Linear · Quadratic · Absolute value
Show solution
- Constant percent change.
Answer: Exponential
4. A value starts at 120 and decays by 15%. What multiplier is used?
Show solution
- Decay multiplier is 1 - 0.15.
Answer: 0.85
5. Outputs 3, 6, 12, 24 suggest which model family?
Choices: Exponential · Linear · Quadratic · Constant
Show solution
- Each output is multiplied by 2.
- A constant ratio points to an exponential model.
- So the model family is exponential.
Answer: Exponential
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