Average Rate of Change
Definition
The average rate of change calculates how much one variable changes in relation to another variable over an interval. It measures the slope or steepness between two points on a graph.
Analogy
Think about going up and down stairs in your house. The average rate of change would be like calculating how many steps you climb per second while going from the first floor to the second floor.
Related terms
Instantaneous Rate of Change: Instantaneous rate of change refers to how fast something is changing at any given moment or specific point. It is represented by finding the derivative.
Delta Notation (∆): Delta notation (∆) indicates a difference or change in value between two variables. In terms of average rate of change, it represents the change in y divided by the change in x over an interval.
Linear Function: A linear function is a mathematical equation that represents a straight line. It has a constant rate of change, meaning the average rate of change remains the same throughout.
"Average Rate of Change" appears in:
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Practice Questions (14)
Which formula is used to calculate the average rate of change of a function over a certain interval?
What does the average rate of change measure?
What is the relationship between the average rate of change and the instantaneous rate of change?
The temperature of a room is recorded every hour for 6 hours. The temperature at each hour is as follows: 20°C, 22°C, 24°C, 23°C, 21°C, 20°C. Calculate the average rate of change of temperature from the second hour to the fifth hour.
A car travels at a constant speed of 60 miles per hour for 3 hours and then slows down to 30 miles per hour for 2 hours. Calculate the average rate of change of the distance traveled with respect to time.
The population of a town is recorded every year for 5 years. The population (in thousands) for each year is as follows: 100, 120, 150, 180, 200. Calculate the average rate of change of population from the first year to the last year.
The height of a ball thrown in the air is given by the function h(t) = -16t^2 + 64t, where h(t) represents the height (in feet) at time t (in seconds). Calculate the average rate of change of the position from t = 0 to t = 3.
The position of a moving object is given by the function s(t) = 2t^3 - 9t^2 + 12t, where s(t) represents the position at time t. Calculate the average rate of change of the position from t = 1 to t = 3.
What is average rate of change formula?
Which of the following statements is true regarding the relationship between the average rate of change and the instantaneous rate of change of a function?
Consider the function f(x) = 2x^3 + 5x^2 - 3x. What is the average rate of change of f(x) over the interval [1, 3]?
Consider the function f(x) = 3x^2 - 2x + 1. What is the average rate of change of f(x) over the interval [1, 4]?
The function f(x) = 2x + 3 represents the position of an object at time x. What is the average rate of change of the object's position over the interval [2, 5]?
The temperature T (in degrees Celsius) of a cup of coffee after t minutes is given by the function T(t) = 2t + 20. What is the average rate of change of the temperature of the coffee over the interval [5, 10]?
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