Question

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

Given the number of contestant in each round:

X 1 2 3 4 5

F(x) 243 81 27 9 3

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.