Question

Hadara built the linear function y=5x+8 to model the number of customers a restaurant serves over time (in hours). With this context in mind, what does the average rate of change of the function over the interval 0 to 3 represent?

Answer 1

The average rate of change of the function y = 5x + 8 over the interval 0 to 3 represents the average increase in the number of customers served by the restaurant per hour during that time period.

Step-by-step explanation:

The average rate of change of the function y = 5x + 8 over the interval 0 to 3 represents the average increase in the number of customers served by the restaurant per hour during that time period.

To find the average rate of change, we need to calculate the difference in the number of customers served between the starting and ending points, and then divide that by the difference in time (3 hours in this case).

In this case, the starting point is when x=0 (0 hours), and the ending point is when x=3 (3 hours). So, the average rate of change is: (y2 - y1)/(x2 - x1) = (5(3) + 8 - (5(0) + 8))/(3 - 0) = (15 + 8 - 8)/3 = 7/3 = 2.33 customers per hour.