The given data represents the number of days (1-7) and their corresponding run times in hours. To find the function that best represents the data, we need to analyze the pattern and trend in the run times. A non linear function best represents the data.
Looking at the data, we can see that the run times are decreasing gradually from day 1 to day 7. Therefore, we can conclude that the data represents a decreasing function.
The given data represents a decreasing trend, and a non-linear function would be the most appropriate to represent the data. However, without more information or data points, it is difficult to determine the specific function that best fits the data.
To find the specific function, let's calculate the average run time for each day:
- Day 1: 8.2
- Day 2: 8.1
- Day 3: 7.5
- Day 4: 7.8
- Day 5: 7.4
- Day 6: 7.2
- Day 7: 7.1
Now, let's plot the points on a graph to visualize the trend:
(1, 8.2)
(2, 8.1)
(3, 7.5)
(4, 7.8)
(5, 7.4)
(6, 7.2)
(7, 7.1)
By connecting these points, we can observe that the data points form a curved line, suggesting that a non-linear function is likely the best fit for the data.
There are several non-linear functions that could fit this data, such as exponential or quadratic functions. Without more information or additional data points, it is challenging to determine the exact function that best represents the data.