Final answer:
To find the average rate of change of the inches of rainfall represented by the function f(x) = 2x-4 + 3 between the 3rd and 10th year, calculate the slope between the two points in the given function. The calculation results in an average rate of change of 2 inches of rainfall per year.
Step-by-step explanation:
The student asks about finding the average rate of change of a function representing inches of rainfall in a rainforest, specifically between the 3rd and 10th year. The important information in this problem is the function f(x) = 2x-4 + 3, and the years we're interested in (the 3rd and 10th year). To find the average rate of change, we would use the formula for the slope between two points on a linear function, which is (f(b) - f(a)) / (b - a), where a is the starting value (3rd year) and b is the ending value (10th year).
The average rate of change from the 3rd to the 10th year can be calculated by substituting x with 3 and 10 into the given function. So we find f(3) = 2(3)-4 + 3 and f(10) = 2(10)-4 + 3, and then subtract f(3) from f(10), and divide by (10 - 3) to get the average rate of change.
This process yields f(3) = 6-4 + 3 = 5 and f(10) = 20-4 + 3 = 19. Therefore, the average rate of change is (19 - 5) / (10 - 3) = 14 / 7 = 2 inches of rainfall per year.