Question

Please help!
Find the average rate of change over the given interval. f(x)=2^x, [3, 5]

Answer 1

Answer: 12

Work Shown

The interval notation [3, 5] means 3 ≤ x ≤ 5

Plug x = 3 and x = 5 into the function to find f(3) = 8 and f(5) = 32.

Then we use the average rate of change formula.

`\text{AROC} = \text{average rate of change}\\\\\text{AROC} = (f(b)-f(a))/(b-a)\\\\\text{AROC} = (f(5)-f(3))/(5-3)\\\\\text{AROC} = (32-8)/(5-3)\\\\\text{AROC} = (24)/(2)\\\\\text{AROC} = 12\\\\`

Alternatively, you can use the slope formula to find the slope of the straight line through the endpoints (3,8) and (5,32).