Rates of Change


How do you find the rate of change?

1 year ago


130 Replies




Vickie Shanahan

130 Answers

Tom K

The rate of change is looking for the amount something would change per unit of time (seconds usually)

This can often be found by dividing what you are changing by how long it takes to change (dividing by the time)

If I had a bath tub with a hole in it with water falling out we could find the rate of change of the amount water in the bath tub

If the bath tub started with 100 litres and lost 30 litres in 1 minute

We could do 30 litres divided by 60 seconds giving a rate of change of 0.5 litres per second

I hope this helps!

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Examples of rates of change are speed (how far you travel over time) and acceleration (how your speed changes over time).

The maths for this is taken from the words.

For example if you travel 150 miles in 2 hours - you divide 150 by 2 - this gives you 75.

The units are miles per hour.

Answer is therefore 75 miles per hour (mph)

Work backwards to check.

If I travel for 2 hours at 75 mph. How far do I travel?

So I travel 75 miles in the first hour and 75 in the second hour .

The total travelled in 2 hours is 75 + 75 miles (or 75 x2).

Giving the answer 150 miles.

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Michail Lazos

The rate of change is difference of y divided by difference of x. In other words it is the derivative at a given point.

Leon Cragg

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

Yunho Kwon

Linear functions have a constant rate of change which is represented as the gradient of the graph.

It is simply the change of y-values with respect to x-values i.e. (y1-y2) / (x1-x2) where (x1,y1), (x2,y2) are the coordinates

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You would have to differentiate

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

Stavros Savva

Divide the change of one variable with the change of the other variable


How do find the rate of change

Will Booth

Rate of change is how quickly a measured quantity (e.g. speed) changes in time. To calculate this you need the change in the quantity (e.g. change in speed = final speed - initial speed) and then you need to divide that result by the change in time i.e. the time over which the measured quantity has changed.

E.g. to calculate the acceleration (rate of change of speed) of a car going from 5m/s to 10m/s in 20s you would do:

Acceleration = (10-5)/20 = 0.25m/s^2

Mohammed Ali

The rate of change can be defined by the following formula

rate of change = (change in quantity 1) / (change in quantity 2).

An example is the distance travelled by a car in a certain amount of time.

Faizan Ahmed

For a linear set of values the rate of change will be the change in y-values divided by the change in x-values in other words the gradient of a straight line. In the set of values relating to a curved line the rate of change on each point can be found by differentiating the equation of that curve and using the values of x of the point you need to find the rate of change at.

Santosh Rimal

we can find through gradient in graph or by calculation of numbers

Holly Willis

change in y over the change in x

Soumyadeep Mukherjee

Rate of change of any property is given by the change in the value of property per unit time. For example if the temperature at a location drops 5°C in 5 minutes. Then the rate of temperature is 5/5 °C/min i.e. 1 °C/min

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