Final answer:
The average rate of change of the function y = 1 + 3x + 0.5x² between x = 6 and x = 8 is 10.
Step-by-step explanation:
To find the average rate of change of the function y = 1 + 3x + 0.5x² between x = 6 and x = 8, we need to calculate the change in y divided by the change in x.
First, find the y-values at x = 6 and x = 8 by substituting the given values into the function: y(6) = 1 + 3(6) + 0.5(6)² = 1 + 18 + 18 = 37 and y(8) = 1 + 3(8) + 0.5(8)² = 1 + 24 + 32 = 57.
Next, calculate the change in y and x: Δy = 57 - 37 = 20 and Δx = 8 - 6 = 2. Finally, divide the change in y by the change in x to find the average rate of change: (Δy)/(Δx) = 20/2 = 10.