Question

Give an example where the concept of "rate of change" is used in real life.

Answer 1

Before considering the real life example of rate of change we initialy explan its concept.

Consider two sets A and B as

So the first set contain all possible values of circumference where as the second set contain all possible values of radius.

Now we can define a relationship between these two sets . The circumference of the circle depends on the radius as follows

Here both C and r can vary but

The circumference change only when there is a change in radius hence we can say

Radius (r) is the independent variable and the circumference (c) is the dependent variable.

The Rate of Change of C with respect to r measures the speed at which C changes as r varies.

As an example consider a man who is driving to a town from his home. As the time t changes the distance between him and his home, let it be s ; changes. Now we can say how fast this s changes gives the speed at which he is driving.

The rate of change of distance with respect to time

If there is no change in 's' as time changes then we can say that he is not moving.

Another example is climatic change

Green house gases is the main factor that causes green house effect. We know as the concentration of green house gases increase in the atmosphere then it will increase the green house effect. Hence it will result in global warming.

The rate of change in the phenomenon of global warming is depends on the concentration of green house gases in the atmosphere.

Basically for defining rate of change of a variable, we need another variable to which it depends on.