Question

What is the average rate of change for this exponential function for the interval from x=2 to x=4?

Answer 1

Use slope for (y2-y2/x2-x1) to find the average slope.

Plug 4 into the function. The answer is y2 (4 is x2)

Plug 2 into the function. The answer is y1 (2 is x1)

(y2 - y1)/ (4 - 2)

(y2 - y1)/2

That is how you would get the average rate of change.

Answer 2

The equation to calculate the average rate of change is: y/x

y = f(x2) - f(x1)x = x2 - x1

x1: 1 (The smaller x value. It can be any number)x2: 2 (The larger x value. It also can be any number)f(x1): The value when you plug x1 into the function.f(x2): The value when you plug x2 into the function.

If we know this, the variables for this problem are assuming the function is 10(5.5)^x:

x2: 2x1: 1f(x2): 10(5.5)^(2) = 302.5f(x1): 10(5.5)^(1)= 55

This means:y = 302.5  - 55 = 247.5x = 2 - 1 = 1

Remember: the equation for avg rate of change is y/x

So, our average rate of change for the function on the interval [1,2] is 247.5 (y/x = 247.5/1)