Question

URGENT A dance competition on television had five elimination rounds. After each elimination, only one-fourth of the contestants were sent to the next round. The table below shows the number of contestants in each round of the competition:

x 1 2 3 4 5
f(x) 512 128 32 8 2


Compute the average rate of change of f(x) from x = 2 to x = 4, and describe what it represents.

Answer 1

Use the idea of slope here to find the rate of change of contestants since that is what slope is: the average rate of change between two coordinates. This is not linear, so the rate of change for the whole function is not going to be the same as it is between round 2 and round 4. The slope formula using the coordinates from x = 2 to x = 4 is 8 - 128/4 - 2 which gives a slope of -60. This represents the average rate of change of contestants from the second round to the fourth.

Answer 2

Average rate of change in given function from x = 4 to x = 2 is -60.

Explanation:

We are given the following information in the question:

x: 1 2 3 4 5

f(x): 512 128 32 8 2

Formula:

`\text{Average rate of change of function} = \displaystyle(f(y)-f(x))/((y-x))`

Putting the values,

`\text{Rate of change given function from x=2 to x=4} = \displaystyle(f(4)-f(2))/((4-2))\\\\ =(8-128)/(4-2)\\\\ =(-120)/(2) = -60`

Hence, average rate of change in given function from x = 4 to x = 2 is -60.