# The Average Rate of Change of Function

Here is the question: The following chart shows the growth of a crowd at a rally over a 3 h period.

• Time (in hours): $0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0$
• Number of people: $0 , 176, 245, 388, 402, 432, 415$

a) Determine the average rate of change in the size of the crowd for each half hour of the rally

b) What do these numbers represent?

So with this question I should be able to use $\Delta f(x)/\Delta x= (f(x_2) - f(x_1))/(x_2-x_1)$ as my formula to solve this. However, I am not sure since there is not a given interval like most other questions I have done. In this case it tells you that it is over a 3 hour period and it wants the Average rate of change for each 1/2 hour.

Yes, there is a given interval. The interval between each measurement and the next is $1/2$ hour. That is the interval you are being asked to measure the average growth over.
• so since it asks for each 1/2 hour, does this mean I would have to do each of them so example: $f(x2)-f(x1)/x2-x2 = 176(0.5)-0(0)/0.5-0$. And then continue this using the rest of the values in the chart? – Ash Apr 24 '15 at 0:24