How do you find the rate of change?

Let's start by discussing what rate of change is: Rate of Change refers to how one variable changes with respect to another variable. In GCSE, it would most likely be change in y with respect to change in x.

In practical terms, think of how when you’re watching videos on your laptop and your battery drops gradually.

So, if you'd like to find the rate of change of battery percentage from 100% to 70% in 1 hour (where y = battery percentage and x = time)

(70% - 100%)/1 = -30% per hour

or

(70% - 100%)/60 = -0.5% per minute

The general formula would be "change in y /change in x" or "(final y - initial y)/ (final x - initial x)". Please let me know if you'd like any more clarification on this.

The rate of change in measured the change in Y over the change in X

Difference divided by the time.

In terms of a graph, this will be the change in the y-axis divided by the change in the x-axis (aka slope).

It is simply a total concerned amount divided by the total time. For example, if you want to find out rate of change of distance. You consider total distance covered by the vehicle and divide it by the total time it took for that change.

Rate of change of position = total covered distance / total taken time.

This is easier to work out from a graph, the rate of change is the gradient of the line - the change in y divided by the change in x. However, you might not have time in exam conditions to draw a graph when it's not asked of you, so I would suggest picking two points of the data - ignoring outliers if there are any. Calculate the difference between them by taking them away from each other, then divide that by the difference in time between them. This will give you the rate of change.

In a graph of a value vs time, it would be the gradient. Otherwise simply divide the difference in any particular value by the time taken.

If you take the change in Y values and divide that with the change in X-values the result will be a rate of change,

The rate of change (ROC) is how much the value of something changes over a period of time and it is given in percentage terms.

To find this you first calculate the change in "Y" values (or the change in an outcome variable) divided by the change in "X" values (or the change in input variables).

So if my tutoring time increases from 3 hours in week 1 to 16 hours in week 2 and my income increases from £45 per week to £240 per week, Y values are my income and X values are the work hours I put in. r

To calculate the ROC I would do the following.

(240 - 45) / (16 - 3) = 195 / 13 = 15% rate of change in my earnings between week 1 and week 2.

You would have to differentiate

This depends on what type of rate of change you are looking for, however either it be speed, temperature or mass, you are usually able to plot this variable against time on a graph, to find the rate of change you have to find the gradient of this graph.

If looking at a straight line graph, you are able to simply identify two points on the line and note down their coordinates. You are then able to do (Y2-Y1)/(X2-X1) to find the rate of change.

If it is a curved graph, draw a tangent and use the (Y2-Y1)/(X2-X1) formula on the tangent. The rate of change is not the same all across and you have to draw a tangent on a specific point on the graph to find the rate of change at that time specifically.

You would also be able to use differentiation to be able to find the gradient at a specific point.

I hope this helps :)

The rate of change measures how a quantity changes over time or across space. It's often represented as the slope of a line connecting two points on a graph.

Frays of change is how much x. Ganges w time or another variable . So this can be done by working out the gradient of a graph or differentiating If it is an expression

Distance traveled divided by time it takes. On a graph that would be calculating the difference in the change in y and the change in x

The rate of change (ROC) is the speed at which a variable changes over a specific period of time

divide the change in y-values by the change in x-values