Question

A wrestling match has eliminations each round. The table below shows the number of wrestlers in each of the first 4 rounds of the tournament:

Round (x) 1 2 3 4
Wrestlers f(x) 64 32 18 9

Compute the average rate of change of f(x) from x = 1 to x = 4 and identify the meaning of that rate.

A. 55; there were 55 fewer wrestlers between rounds 1 and 4
B. 3; there were 3 rounds between rounds 1 and 4
C. negative fifty five over three; on average, there were 55 fewer players for every 3 rounds
D. negative three over fifty five; on average, there were 3 fewer players for every 55 rounds

Answer 1

I think it might be C. Hope this helps :)

Answer 2

Answer: Option C is correct.The average rate of change of f(x) from x = 1 to x = 4 negative fifty five over three; on average, there were 55 fewer players for every 3 rounds .

Explanation:

Given: A wrestling match has eliminations each round.

From the table given in the question

Average rate of change=
`\frac{\text{change in f(x)}}{\text{change in x}}=(f(x_4)-f(x_1))/(x_4-x_1)=(9-64)/(4-1)=(-55)/(3)`

Therefore, the average rate of change of f(x) from x = 1 to x = 4=
`(-55)/(3)`, which means there were 55 fewer players for every 3 rounds .

Average rate of change is the change in the value of f(x) divided by change in the value of x for two distinct points on the graph.