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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.

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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.

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  • $\begingroup$ 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? $\endgroup$ – Ash Apr 24 '15 at 0:24
  • $\begingroup$ That is correct. Then you have to think about whether the increase should be stated as "per half hour" or "per hour (measured over a half hour)". While this might sound strange, if I asked for the average speed of a car over a half hour, I would expect the answer to be XXX miles (or kilometers) per hour. This is an English question, not a mathematical one. $\endgroup$ – Ross Millikan Apr 24 '15 at 0:27
  • $\begingroup$ Okay! Thanks a lot. That's a lot of help. $\endgroup$ – Ash Apr 24 '15 at 0:29

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