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.
55; there were 55 fewer wrestlers between rounds 1 and 4
3; there were 3 rounds between rounds 1 and 4
negative fifty five over three; on average, there were 55 fewer players for every 3 rounds
negative three over fifty five; on average, there were 3 fewer players for every 55 rounds
To compute the average rate of change of f(x) from x = 1 to x = 4, we need to find the difference in f(x) values and divide it by the difference in x values.
The difference in f(x) values is:
f(4) - f(1) = 9 - 64 = -55
The difference in x values is:
4 - 1 = 3
Therefore, the average rate of change is:
-55/3
The meaning of this rate is that on average, there were 55 fewer wrestlers for every 3 rounds.
To compute the average rate of change of f(x) from x = 1 to x = 4, you need to find the difference in the values of f(x) between those two points and divide it by the difference in the x-values.
In this case, the difference in f(x) is 9 - 64 = -55 (since there were 55 fewer wrestlers between rounds 1 and 4), and the difference in x-values is 4 - 1 = 3 (since there were 3 rounds between rounds 1 and 4).
Therefore, the average rate of change of f(x) from x = 1 to x = 4 is -55/3.
So, the correct answer is: negative fifty five over three; on average, there were 55 fewer wrestlers for every 3 rounds.