Question

Water coming out from a fountain is modeled by the function f(x) = -x2 + 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?

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

Answer 1

average rate of change is given by the change of y over the change of x.
\[\frac{ f(5)-f(3)}{5-3} \]

Answer 2

you are dividing a change of height by a change in time

Answer 3

So x = 2?

Answer 4

also "rate of change" = speed

Answer 5

So, I know its either A or B, right?

Answer 6

yes

Answer 7

So its either 5 or 3 feet per 3-5 seconds?

Answer 8

just used the formula I gave above to figure out between A and B

Answer 9

I dont understand the formula you gave me.

Answer 10

f(5) - f(3) = f(2)
-----
2
??????????????

Answer 11

...how did you get f(5)-f(3)=f(2)?

Answer 12

f(5)=-5^2+5(5)+4
and
f(3)=-3^2+5(3)+4

Answer 13

So f(5) = 3154
And f(3) = 110

Answer 14

-5^2+5(5)+4
------
first we know 5^2=5(5)=25
so
-5^2+5(5)+4
can be written as
-25+25+4

Answer 15

-25+25 is 0 though
so you have
-5^2+5(5)+4
can be written as
0+4
which is just 4

Answer 16

can you try doing f(3)

Answer 17

f(3) = 25?

Answer 18

are you guessing?

Answer 19

No

Answer 20

f(x)=-x^2+5x+4
just plug in 3 where x is

Answer 21

OH there is a negative, my bad

Answer 22

f(3)=-3^2+5(3)+4
3^2 means 3(3) which is 9
5(3) is 15
f(3)=-9+15+4

Answer 23

so 10?

Answer 24

\[\frac{f(5)-f(3)}{5-3}=\frac{4-10}{5-3}\]

Answer 25

so its 3

Answer 26

So the answer is a?

Answer 27

well -3 where the units is distance/time which is a speed unit
which just means going down at a speed of 3ft/sec

Answer 28

and yes a sounds great

Answer 29

Thx for the help! Ima submit my test now, lets see :D

Answer 30

Oh no! I got a %62 on my test :(. 5 questions wrong out of 13. But the one you helped me with was right, ty so much!