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: 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 .

Step-by-step explanation:

Given: A wrestling match has eliminations each round.

From the table given in the question

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

Therefore, the average rate of change of f(x) from x = 1 to x = 4=[tex]\frac{-55}{3}[/tex], 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.