Respuesta :
Answer:
To find the average rate of change for the function
=0.0
2
f(x)=0.08x
2
over the interval
10
≤
≤
20
10≤x≤20, we need to find the change in height divided by the change in distance over that interval.
Step-by-step explanation:
To find the average rate of change for the function
�
(
�
)
=
0.08
�
2
f(x)=0.08x
2
over the interval
10
≤
�
≤
20
10≤x≤20, we need to find the change in height divided by the change in distance over that interval.
The change in height over the interval is given by
�
(
20
)
−
�
(
10
)
f(20)−f(10), and the change in distance is
20
−
10
20−10.
We'll start by evaluating the function
�
(
�
)
=
0.08
�
2
f(x)=0.08x
2
at
�
=
20
x=20 and
�
=
10
x=10:
At
�
=
20
x=20:
�
(
20
)
=
0.08
×
(
20
)
2
=
0.08
×
400
=
32
f(20)=0.08×(20)
2
=0.08×400=32 meters
At
�
=
10
x=10:
�
(
10
)
=
0.08
×
(
10
)
2
=
0.08
×
100
=
8
f(10)=0.08×(10)
2
=0.08×100=8 meters
The change in height is
32
−
8
=
24
32−8=24 meters.
Now, we'll find the change in distance, which is
20
−
10
=
10
20−10=10 kilometers.
The average rate of change is the change in height divided by the change in distance:
�
=
24
meters
10
kilometers
=
2.4
meters per kilometer
A=
10 kilometers
24 meters
=2.4 meters per kilometer
So, the average rate of change for the function over the interval
10
≤
�
≤
20
10≤x≤20 is
2.4
2.4 meters per kilometer.
