Respuesta :
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.
Answer:
Average rate of change is -78.
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 [tex]\dfrac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
So, the average rate of change of [tex]f(x)[/tex] from [tex]x = 1[/tex] to [tex]x = 4[/tex] is,
[tex]=\dfrac{f(4)-f(1)}{4-1}[/tex]
[tex]=\dfrac{9-243}{4-1}[/tex]
[tex]=\dfrac{-234}{3}[/tex]
[tex]=-78[/tex]
Since f(x) is decreasing, so rate of change is negative.