Water coming out of a fountain is modeled by the function f (x) = - x^2 + 5x + 4 where f (x) represents the height, in feet, of the water from the fountain at different times x, in seconds. What does the average rate of change of f (x) from x = 3 to x = 5 represent?

A. The water falls down with an average speed of 3 feet per second from 3 seconds to 5 seconds.

B. The water falls down with an average speed of 5 feet per second from 3 seconds to 5 seconds.

C. The water travels an average distance of 3 feet from 3 seconds to 5 seconds.

D. The water travels an average distance of 5 feet from 3 seconds to 5 seconds.

Question

Maia Melendez

Mathematics

10 November, 16:41

Water coming out of a fountain is modeled by the function f (x) = - x^2 + 5x + 4 where f (x) represents the height, in feet, of the water from the fountain at different times x, in seconds. What does the average rate of change of f (x) from x = 3 to x = 5 represent?

A. The water falls down with an average speed of 3 feet per second from 3 seconds to 5 seconds.

B. The water falls down with an average speed of 5 feet per second from 3 seconds to 5 seconds.

C. The water travels an average distance of 3 feet from 3 seconds to 5 seconds.

D. The water travels an average distance of 5 feet from 3 seconds to 5 seconds.

+4

Answers (1)

Know the Answer?

Natalie Mason · Answer 1

Calculating x=3 and x=5, we get f (x) = 10 and 4 respectively by plugging the numbers into the equation. Finding the difference and dividing by 2 (since there are 2 seconds between 3 and 5), we get 3, so the answer is either A or C. Since it doesn't only fall 3 feet, we need to specify that it is 3 feet per second, A is right!