Average Rate of Change
Average Rate of Change
One way to describe how a quantity changes over some interval. is the average rate of
change. The average rate of change of the function f(t) over the interval from t= a to t= b is
given by
Consider, for example, the function
which can be used to model the population of Forsyth County, Georgia. The function
describes the population in thousands in the year 2000 + t. \
The average rate of change of a population is the total change divided by the time taken for
that change to occur. The average rate of change can be calculated with only the times and
populations at the beginning and end of the period.
Calculating the average rate of change is similar to calculating the average velocity of an
object, but is different from calculating the instantaneous rate of change.
In the examples below we wil determine the average rate of change of the population of
Forsyth County over two different intervals of time.
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Example 1 :-
What was the average rate of change of the population of Forsyth County between 1990 and
2000?
Solution :-
Since t = -10 corresponds to the year 1990 and t = 0 corresponds to 2000, we first calculate
the change in population between 1990 and 2000 as follows:

Next we divide by the length of time, 2000-1990 = 10 years:
We see that the population of Forsyth County grew at an average rate of 4.098 thousand
people per year between 1990 and 2000.
Example 2
What was the average rate of change of the population of Forsyth County between 1980 and
1990?
Solution
Since t = -20 corresponds to the year 1980 and t = -10 corresponds to 1990, we first calculate
the change in population between 1980 and 1990 as follows:
F(-10) - F(-20) = 22.0788 thousand.
Next we divide by the length of time, 1990
1980 = 10 years:
We see that the population of Forsyth County grew at an average rate of 2.208 thousand
people per year between 1980 and 1990.
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In the above examples, we computed the average rate of change of the function F(t) over the
interval from t = -10 to t = 0 and then again over the interval from t = -20 to t = -10.
You may have noticed that we used the same formula for calculating the average rate of
change as the one we use for calculating the slope of a line between two points. Figure 1
shows a graph of F(t) and the line through the points (-10, F(-10)) and (0, F(0)).
Area of rectangle = Length * Breath.
In general notation area of rectangle is denoted by the symbol `A', the Length of rectangle is
denoted by the symbol `L' and the breath of rectangle is denoted by the symbol `B'. So we can
write as:
A = L. B,
Now we show you the some of the example that helps in understanding the concept of
calculating the area of rectangle.
Example: Find the area of rectangle which has the length of the side is 20m and the breath of
the side is 10m?
Solution: In the above question given that the length of rectangle is 20m and the breadth of
the rectangle is 10 m. So we solve this problem by applying the area of rectangle:
Area of rectangle = Length * Breathe,
A = L * B,
A = 20 * 10,
A = 200m2.
In the above we can see that the area of rectangle can easily be calculated by using the
formula of rectangle. In the above we the power of two with the 200m2.This is done because
in the formula two values of meter are multiplied to each other.


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