Select and interpret a function model
The input is throughput, measured in items per hour, and the output is time per item, measured in seconds. The data describe this situation: the time per item decreases towards a baseline as throughput increases
The following exact data are used over the interval \(x\in\left[1,12\right]\)
| throughput (items per hour) | time per item (seconds) |
|---|---|
| \(1\) | \(56\) |
| \(2\) | \(\frac{274}{5}\) |
| \(3\) | \(54\) |
| \(4\) | \(\frac{374}{7}\) |
| \(5\) | \(53\) |
The output values move towards \(50\) as \(x\) increases. The sizes of the successive changes are \(\frac{6}{5},;\frac{4}{5},;\frac{4}{7},;\frac{3}{7}\)
Which function family is consistent with the complete pattern in the table?