Recognize constant rate situations

What you'll learn

1. Define "constant rate of change" as a fixed amount added (or subtracted) per unit interval, and connect this to the slope of a linear function
2. Identify constant rate situations from verbal descriptions by recognizing key phrases such as "per hour," "each month," "for every," and "at a steady pace"
3. Distinguish constant rate situations (linear) from constant percent rate situations (exponential) when both are described in words
4. Write a linear function f(x) = mx + b from a constant rate description, identifying the rate as slope and the starting value as y-intercept
5. Interpret the rate and initial value in context, including correct units (e.g., "dollars per month," "miles per hour")
6. Evaluate the reasonableness of a linear model by considering whether a constant rate assumption makes sense for the given context

Prerequisites

• Prove growth properties of functions