Question

at a popular three - day sci - fi convention, the event organizers have a main hall that can accommodate 700 visitors at any given time. the convention started at 9:00 am and ran for 12 hours. the organizers recorded the number of visitors, including special guests, throughout the first 8 hours. the data was recorded as a percentage of the maximum capacity and a 4th - degree polynomial function with a coefficient of determination of 0.93 was used to model the halls capacity for the remainder of the event. can the organizers use this function to predict the halls capacity at 10 hours? yes. this function provides a strong model for the data, so making a prediction for the capacity at 10 hours is appropriate. no. even though this function provides a strong model for the data, h = 10 is too far from the known data values and would be considered an extreme extrapolation. no. even though this function provides a strong model for the data, the functions prediction at h = 10 would not be a valid conclusion. yes. we can predict the capacity at h = 10 since a 4th - degree polynomial is the best choice to model the data.

Explanation:

The coefficient of determination ($r^{2}=0.93$) shows a strong fit for the known data (first 8 - hour data). However, predicting at $h = 10$ when data is only recorded for the first 8 hours is extreme extrapolation. Extrapolating too far from the known data range can lead to inaccurate predictions even with a high - $r^{2}$ value.

Answer:

No. Even though this function provides a strong model for the data, h=10 is too far from the known data values and would be considered an extreme extrapolation.