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Ivahew [28]
3 years ago
14

A talent competition on television had five elimination rounds. After each elimination, only one-third of the contestants were s

ent to the next round. The table below shows the number of contestants in each round of the competition.
x12345
f(x)243812793


Compute the average rate of change of f(x) from x = 1 to x = 4 and describe what it represents.
Mathematics
2 answers:
denis-greek [22]3 years ago
8 0

Answer:

<em>Average rate of change is </em><em>-78.</em>

Step-by-step explanation:

A talent competition on television had five elimination rounds. After each elimination, only one-third of the contestants were sent to the next round.

The table that shows the number of contestants in each round of the competition is,

x     f(x)

1      243

2     81

3     27

4     9

5     3

Average rate of change is the change in the y-value divided by the change in the x-value for two points on the graph.

i.e \dfrac{f(x_2)-f(x_1)}{x_2-x_1}

So, the average rate of change of f(x) from x = 1 to x = 4 is,

=\dfrac{f(4)-f(1)}{4-1}

=\dfrac{9-243}{4-1}

=\dfrac{-234}{3}

=-78

Since f(x) is decreasing, so rate of change is negative.

Ugo [173]3 years ago
3 0
For the answer to the question above, 

Given the number of the contestants in each round:

X      1     2     3    4    5

F(x) 243  81  27   9     3

The rate of change can be calculated using y2-y1/x2-x1 formula. From rounds 1 to 4 the rate of change are

-162, -54, -18. And the average of it is -78 and it represents the average rate at which the number of contestants changed from the first round to the fourth round.

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