Question

PLEASE HELP ASAP!!! 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 below shows the number of contestants in each round of the competition: x 1 2 3 4 5 f(x) 243 81 27 9 3 Compute the average rate of change of f(x) from x = 1 to x = 4 and describe what it represents.

A) −78 contestants per round, and it represents the number of contestants who will reach the final round

B)−234 contestants per round, and it represents the number of contestants who will reach the final round

C)−234 contestants per round, and it represents the average rate at which the number of contestants changed from the first round to the fourth round

D) −78 contestants per round, and it represents the average rate at which the number of contestants changed from the first round to the fourth round

Answer 1

(9-243)/(4-1)=-78
D)−78 contestants per round, and it represents the average rate at which the number of contestants changed from the first round to the fourth roundReport · 14/12/2015

Answer 2

D

Explanation:

Given the following data

x 1 2 3 4 5

f(x) 243 81 27 9 3

The rate of change between the second and the first points is computed as

(f(x2) - f(x1))/(x2 -x1) = (81 - 243)/(2-1) = -162

Analogously, between 3rd and 2nd points and between 4th and 3rd points:

27 - 81 = -54

9 - 27 = -18

Therefore, the average rate of change is (-162 -54 -18)/3 = -78 contestants per round, and it represents the average rate at which the number of contestants changed from the first round to the fourth round .