1.12 Modeling Variation
Ideas in this lesson
- Recognize direct and inverse variation
- Translate variation statements into equations
- Determine and interpret the variation constant
- Predict values and solve for inputs
- Combine proportional changes
- Model joint and inverse-square relationships
- Build power, root, and multivariable scientific models
- Choose meaningful variables and test modeling assumptions
Recognize direct and inverse variation · Worked example
For positive inputs, a table gives \((x,y)=(1,12),(2,6),(4,3)\). Which model and invariant fit every pair?
Answer: \(y=\dfrac{12}{x}\); \(x\,y=12\).
All products are \(12\).
The ratios differ, so the model is not direct variation.
Solve the constant-product relation for \(y\) to obtain \(\dfrac{12}{x}\).
The ratios differ, so the model is not direct variation.
Solve the constant-product relation for \(y\) to obtain \(\dfrac{12}{x}\).