Final answer:
The constant rate of change of the profits with respect to the days is found by calculating the slope of the line that the data points form. By taking two points from the data, the rate is determined to be $3 a day, which is the slope of the line.
Step-by-step explanation:
The question involves finding the constant rate of change for a set of data pairs representing days (x) and profits (y). To determine this rate, we can pick two points from the table and use the formula for the slope of a line, which is the change in y divided by the change in x (also known as rise over run).
We can select points (3, $59) and (8, $74), as an example. To calculate the rate of change, we subtract the profits and days of the first point from the profits and days of the second point. This provides us with: ($74 - $59) /(8 - 3) = $15 / 5 = $3 per day.
Therefore, the constant rate of change, or the amount by which profits increase for each additional day, is $3 a day, which corresponds to option A.