At a factory, the number of produced widgets increased from 500 to 750 from 9am to 12pm. Find the rate of change over the interval 9≤x≤12.
To find the rate of change, you'll need to calculate the difference in the number of widgets produced and divide that by the difference in time.
First, establish the initial number of widgets produced at 9am as "y1" and the final number at 12pm as "y2". In this case, y1 = 500 (at 9am) and y2 = 750 (at 12pm).
Then, determine the time difference between the two points, which is the final time minus the initial time. Here, x1 = 9am and x2 = 12pm. As we are dealing with a 24-hour timeframe, we need to convert these times into a decimal format. Assuming x1 = 9 and x2 = 12 (in hours).
The formula for the rate of change is:
Rate of change = (y2 - y1) / (x2 - x1)
Now, substitute the given values into the formula:
Rate of change = (750 - 500) / (12 - 9)
Simplifying:
Rate of change = 250 / 3 = 83.33 (rounded to two decimal places)
Therefore, the rate of change in the number of produced widgets over the interval 9am to 12pm is approximately 83.33 widgets per hour.