How do you find the rate of change?

Hi, as for rate of change, you need to find two important data - change in quantity 1 and change in quantity 2, and then divide the change1 by the change2 to get the rate of change.

For example, the length of grass in your garden is 1 inch in the 3rd day and the length of grass is 3.5 inches in the 15th day. If you want to figure out the rate of change in grass growth, you will first to calculate the change of length, which is 3.5-1=2.5 inches. Then the change of time= 15-3=12 days. So the result will be: rate of change= 2.5 inches/12 days=0.2 inches per day

If we have a function y = 2x + 3 then the rate of change of that function dy/dx is the slope of the graph of y against x. This is the first derivative. In our case dy/dx = 2.

change in y-values divided by change in x-values

Rate of change = change in y/ change in x

To find rate of change of anything between an interval you just do this:

(Final Value-Initial Value)/Corresponding Time

E.g: If your are trying to find rate of change of speed in a particular interval just subtract the initial value of speed from its final value in that specific interval.

You didn't say which variables you are interested in but here are a couple of examples:

1. Distance / Time - Rate of change (Speed) = distance covered / time taken. So if you wanted the rate of change (speed) in miles per hour - Covering 15 miles in 30 minutes. Would be 30 mph.
2. If you were looking at a straight line then rate of change (gradient) = change in y / change in x. So for a line passing though the points (2,5) and (6,13) , the change in y is (13-5=8) and the change in x is (6-2=4) So the rate of change (gradient) is 8/4 = 2.

Hi Vickie, Rate of Change is defined as the change in some quantity over unit time. For example rate of change of Distance would be speed measured in km/h. Often in a Maths GCSE paper this would involve a question with a graph, for example having Distance on the y-axis and Time on the x-axis. The rate of change would be the gradient of the line on the graph.

This depends on what you mean by the rate of change. In simple terms, the rate of change can be found by finding the change in y and then dividing it by the change in x. For example, if a car travels 60km in 3 hours, the distance (km) traveled will be the y-axis, and time (hours) will be the x-axis. The change in y will be 60km and the change in x will be 3 hours. The rate of change will be 60/3 = 20km/hr

The rate of change can be determined in many different ways and depends on your exam board. If for example, you are taking an IGCSE we could introduce differentiation and differentiate an equation to find the equation's rate of change. If a graph is given we would pick a point on the line, perhaps draw a tangent on the line to determine the gradient and calculate the change in y divided by the change in x.

The rate of change is given by the division of the output of a system y by the change in the x values, which is the input

If we get the explicit equation, we could just differentiate that wrt the variable. If we don’t, we can estimate it by calculating the change on the y-axis and dividing it by the change on the x-axis.

By the help of differentiation

rate of change can be found by using the equation - Difference in Y/ Difference in X

Hi Mrs Shanahan,

Rate of change is also known as the gradient. You can either use calculus to find the rate of change - this would be differentiation - and there are a range of methods you can use. These should be listed in your specification either in IGCSE, further maths GCSE, or A-Level.

A non-calculus method, more commonly known to those who are not studying at A-Level, is to simply estimate the rate of change. You can do this by taking two points on a linear graph (x1, y1) and (x2, y2) and finding the change in y / change in x. I.e. (y2-y1)/(x2-x1). For a non-linear graph, you can do the same by drawing a tangent at the point you want to find the rate of change and applying the same logic as above.

Hope this helps.

The rate of change refers to how much something for example distance is changing in a specific unit of time. In order to work out the rate of change, you must divide the thing that is changing with how much it has changed in such a unit of time.