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Which statement best describes the situation of the local music festival's attendance growth from 2000 to 2003?

a) A decreasing linear function can be used to describe this situation because it has a decreasing percent change.
b) An increasing exponential function can be used to describe this situation because it has a constant percent change.
c) A decreasing exponential function can be used to describe this situation because it has a decreasing percent change.
d) An increasing linear function can be used to describe this situation because it has a constant percent change.

1 Answer

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Final answer:

Without specific data on the festival's attendance growth, it's not possible to determine if the growth is linear or exponential. However, we can infer it is either an increasing linear function or an increasing exponential function because the attendance is growing. Additional data is needed for a precise characterization.

Step-by-step explanation:

The student's question pertains to the characterization of the growth of attendance at a local music festival from 2000 to 2003. Given the information, the best description of the situation would likely be an increasing linear function or an increasing exponential function since the attendance is growing. Without specific data points or percent changes provided, we cannot conclusively determine which option is correct. However, we can make general assumptions based on typical behavior of such events.

If the growth rate is consistent year to year, this suggests a linear trend, which is described by option (d). A linear function would have a constant rate of change, meaning the festival's attendance increases by the same amount each year. On the other hand, if the festival's attendance has been increasing by a constant percentage, this suggests an exponential trend, which is option (b). An exponential trend in attendance growth means that each year, the attendance is a multiple of the previous year’s.

Overall, without exact figures or knowledge of whether the percent change is constant or decreasing, we cannot determine with certainty if the trend is linear or exponential. However, since the question refers to growth, options (a) and (c), which mention decrease, can be ruled out.

To definitively characterize the attendance growth, additional data such as the actual numbers or percentages of growth for the specific years in question would be required.

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