Rate of change

Learning Objectives Define 'rate of change' in their own words. Identify the independent and dependent quantities in a rate of change problem. Calculate the average rate of change from given data. Determine the correct units for a calculated rate of change. Interpret the meaning of a rate of change in a real-world scenario. Solve simple real-world problems involving average rate of change. Ever wonder how fast a plant grows 🌱 or how quickly your phone battery drains 🔋? That's all about 'rate of change'! In this lesson, you'll discover how to measure and understand how one quantity changes in relation to another. This skill helps us make sense of the world around us, from speed to prices, and is a fundamental concept in mathematics. Real-Worl...

TermDefinitionExample RateA ratio that compares two quantities measured in different units.If you drive 60 miles in 1 hour, your rate is 60 miles per hour. Rate of ChangeA rate that describes how one quantity changes in relation to another quantity. It tells us how much the dependent quantity changes for each unit change in the independent quantity.A temperature increase of 2 degrees Celsius per hour is a rate of change. Independent Quantity (Variable)The quantity that causes the change or is controlled. It's often the 'input' and usually measured along the horizontal axis in a graph.In a problem about distance traveled over time, 'time' is the independent quantity. Dependent Quantity (Variable)The quantity that changes as a result of the independent quantity. It&...

General Rate Formula $ ext{Rate} = \frac{ ext{Quantity 1}}{ ext{Quantity 2}}$ Use this to express how much of one quantity there is for each unit of another quantity. Remember to include units! Average Rate of Change Formula $ ext{Average Rate of Change} = \frac{ ext{Change in Dependent Quantity}}{ ext{Change in Independent Quantity}}$ This is the primary formula for finding how one value changes with respect to another. Always subtract the initial value from the final value for both quantities. Calculating Change $ ext{Change} = \text{Final Value} - \text{Initial Value}$ Use this to find the difference between two values for either the dependent or independent quantity before applying the rate of change formula.