Rate of Change

Front

What is the definition of rate of change?

Back

The rate of change is a measure of how a quantity changes in relation to another quantity, often expressed as a ratio or a derivative.

Front

How do you calculate the rate of change between two points on a graph?

Back

The rate of change can be calculated by taking the difference in the y-values and dividing it by the difference in the x-values (slope formula: (y2 - y1) / (x2 - x1)).

Front

What is the significance of a positive rate of change?

Back

A positive rate of change indicates that the quantity is increasing over the interval considered.

Front

What does a negative rate of change signify?

Back

A negative rate of change indicates that the quantity is decreasing over the interval considered.

Front

What is the average rate of change?

Back

The average rate of change is the total change in a quantity divided by the total time over which the change occurred.

Front

In the context of a function, what does the derivative represent?

Back

The derivative represents the instantaneous rate of change of a function at a given point.

Front

What are some common applications of rate of change in real life?

Back

Applications include speed (distance over time), economic growth (change in GDP), and population growth (change in population over time).

Front

How can you interpret the slope of a line on a graph?

Back

The slope of a line represents the rate of change between the two variables plotted on the graph.

Front

What is the formula for calculating the slope of a line?

Back

The formula for calculating the slope (m) is m = (y2 - y1) / (x2 - x1).

Front

What does it mean if the rate of change is zero?

Back

A rate of change of zero indicates that there is no change in the quantity over the interval considered.