Question

What is the approximate average rate of change of the function f(x) = 3(0.5)^x over the interval x = 3 to x = 6?

a) 0.75
b) 1.13
c) 1.69
d) 2.54

Answer 1

The average rate of change of f(x) = 3(0.5)^x over the interval x = 3 to x = 6 is calculated as -0.109375 via the formula [f(x2) - f(x1)] / (x2 - x1). There may be an error in the provided options or in the calculation since this result does not match any of the options.

Step-by-step explanation:

To determine the approximate average rate of change of the function f(x) = 3(0.5)^x over the interval from x = 3 to x = 6, you utilize the formula for average rate of change, which is:

Average Rate of Change = [f(x2) - f(x1)] / (x2 - x1)

Where x1 is the starting point and x2 is the ending point of the interval.

First, calculate the functional values at the endpoints of the interval:

• f(3) = 3(0.5)^3 = 3(0.125) = 0.375
• f(6) = 3(0.5)^6 = 3(0.015625) = 0.046875

Now apply the values to the average rate of change formula:

Average Rate of Change = [f(6) - f(3)] / (6 - 3)
= (0.046875 - 0.375) / (6 - 3)
= -0.328125 / 3
= -0.109375

Therefore, the average rate of change is approximately -0.109375, which is not one of the options provided.