A music competition on television had five elimination rounds. After each elimination, only half 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) 64 32 16 8 4 Compute the average rate of change of f(x) from x = 3 to x = 5 and describe what it represents. −6 contestants per round, and it represents the number of contestants who will reach the final round −28 contestants per round, and it represents the number of contestants who will reach the final round −6 contestants per round, and it represents the average rate at which the number of contestants decreased from the third round to the fifth round −28 contestants per round, and it represents the average rate at which the number of contestants decreased from the third round to the fifth round

m = (Y-y)/(X-x)
m = (4-16)/(5-3)
m = -12/2
m = -6
it represents the average rate at which the number of contestants decreased from the third round to the fifth round

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PratikshaS PratikshaS · Answer 2 · 2022-06-23T11:31:34+02:00

The average rate of change is -6 contestants per round and it represents the average rate at which the number of contestants decreased from the third round to the fifth round.

What is average rate of change?

"It is a measure of how much the function changed per unit, over an interval."

Formula of average rate of change:

To find the average rate of change of a function f(x) in the interval [a, b],

[tex]r=\frac{f(b)-f(a)}{b-a}[/tex]

For given question,

We have been given a table.

x f(x)

1 64

2 32

3 16

4 8

5 4

We need to find the average rate of change of f(x) from x = 3 to x = 5 .

Here, a = 3 and b = 5

For a = 3,

⇒ f(a) = f(3)

⇒ f(a) = 16

And for b = 5,

⇒ f(b) = f(5)

⇒ f(b) = 4

Using the formula of average rate of change,

[tex]\Rightarrow r=\frac{f(b)-f(a)}{b-a}\\\\\Rightarrow r=\frac{4-16}{5-3}\\\\\Rightarrow r=\frac{-12}{2}\\\\\Rightarrow r=-6[/tex]

So, the average rate of change is -6 contestants per round.

This average rate of change represents the average rate at which the number of contestants decreased from the third round to the fifth round.

Therefore, the average rate of change is -6 contestants per round and it represents the average rate at which the number of contestants decreased from the third round to the fifth round.

Learn more about average rate of change here:

https://brainly.com/question/23715190

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