Final answer:
To solve the student's question, values for a, b, f(a), and f(b) are substituted into the slope formula, yielding the average rate of change as 27.5 for the interval x = 2 to x = 2.5.
Step-by-step explanation:
The question given involves the concept of substitution in algebraic expressions or equations. To answer the student's task, we need to substitute the values of a, b, f(a), and f(b) into a given equation that represents the average rate of change or slope. The provided example resembles the calculation of an average rate of change or slope, which is the change in function value (f(b) - f(a)) over the change in variable value (b - a).
Follow these steps to substitute correctly:
- Identify the values for a (2), b (2.5), f(a) (30), and f(b) (43.75).
- Replace these values in the appropriate spots in the equation.
- Perform the mathematical operation to find the result.
In this case, after substitution, the equation would be:
(2.5 - 30)/(2.5 - 2) = (43.75 - 30)/(2.5 - 2)
This simplifies to:
(13.75)/(0.5) = 27.5
Thus, the average rate of change of the function between x = 2 and x = 2.5 is 27.5.