The following table represents the altitude of a hiker climbing a mountain over a 60-minute hike. Calculate the average rate of change over the interval from 0 to 30 minutes.
time (min)
altitude (It)
0
15
30
45
60
1
42
91
105
121
(1 point)
• The rate of change is about 3 feet per minute
O The rate of change is about 30 feet per minute.
O The rate of change is about 2 feet per minute
IC The rate of change is about 90 feet per minute
To calculate the average rate of change over the interval from 0 to 30 minutes, we need to find the change in altitude and divide it by the change in time.
At 0 minutes, the altitude is 1 ft.
At 30 minutes, the altitude is 91 ft.
So, the change in altitude is 91 - 1 = 90 ft.
The change in time is 30 - 0 = 30 minutes.
Therefore, the average rate of change is 90 ft / 30 min = 3 ft/min.
Thus, the correct answer is: The rate of change is about 3 feet per minute. Answer: 3.
A truck is leaving a post office and heading out to deliver mail. The table shows the truck's distanced from the post office at time
t. Calculate the average rate of change over the interval from 8 to 15 minutes
t (min) d (km)
0
8
11
15
22
0
7
11
14
16
(1 point)
© The rate of change is 3.5 kilometers per minute
O The rate of change is 0.8 Kilometers per minute
I© The rate of change is 7 kilometers per minute.
© The rate of change is 1 kilometer per minute
To calculate the average rate of change over the interval from 8 to 15 minutes, we need to find the change in distance and divide it by the change in time.
At 8 minutes, the distance is 7 km.
At 15 minutes, the distance is 14 km.
So, the change in distance is 14 - 7 = 7 km.
The change in time is 15 - 8 = 7 minutes.
Therefore, the average rate of change is 7 km / 7 min = 1 km/min.
Thus, the correct answer is: The rate of change is 1 kilometer per minute. Answer: 1.
Isaac knew he had to study more in order to improve his math grades. Calculate the average rate of change over the interval from his first exam to his third exam using the table below.
Exam Number
1
2
3
4
5
Score (%)
72
75
84
87
94
(1 point)
C The rate of change is 6 percent per exam.
C The rate of change is 12 percent per exam
© The rate of change is 2 percent per exam.
O The rate of change is 5,5 percent per exam
To calculate the average rate of change over the interval from the first exam to the third exam, we need to find the change in score and divide it by the change in exam number.
For the first exam, the score is 72%.
For the third exam, the score is 84%.
So, the change in score is 84 - 72 = 12%.
The change in exam number is 3 - 1 = 2 exams.
Therefore, the average rate of change is 12% / 2 exams = 6% per exam.
Thus, the correct answer is: The rate of change is 6 percent per exam. Answer: 6.
Find the average rate of change over the interval 0 seconds to 60 seconds.
time (sec)
20
40
60
80
length (in.)
120
110
90
60
40
(1 point)
( The rate of change is 2 inches per second.
C The rate of change is -2 inches per second
The rate of change is 1 inch per second
The rate of change is #1 non per second
To calculate the average rate of change over the interval from 0 seconds to 60 seconds, we need to find the change in length and divide it by the change in time.
At 0 seconds, the length is 120 inches.
At 60 seconds, the length is 90 inches.
So, the change in length is 90 - 120 = -30 inches (note the negative sign indicating a decrease in length).
The change in time is 60 - 0 = 60 seconds.
Therefore, the average rate of change is (-30 inches) / (60 seconds) = -0.5 inches per second.
Thus, the correct answer is: The rate of change is -0.5 inches per second. Answer: -0.5.
Find the average rate of change over the interval 2 minutes to 11 minutes.
time (min)
0
12
11
18
20
distance (km)
0
2
5
6
10
(1 point)
O The rate of change is 3 kilometers per minute.
• The rate of change is 4 of a kilometer per minute
• The rate of change is ‡ of a kilometer per minute.
) The rate of change is 3 kilometers per minute
To calculate the average rate of change over the interval from 2 minutes to 11 minutes, we need to find the change in distance and divide it by the change in time.
At 2 minutes, the distance is 5 km.
At 11 minutes, the distance is 6 km.
So, the change in distance is 6 - 5 = 1 km.
The change in time is 11 - 2 = 9 minutes.
Therefore, the average rate of change is 1 km / 9 min ≈ 0.111 km/min.
Thus, the correct answer is: The rate of change is approximately 0.111 kilometers per minute. Answer: ‡ of a kilometer per minute.
To calculate the average rate of change over the interval from 0 to 30 minutes, we need to find the difference in altitude between the two time points and divide it by the difference in time.
The altitude at 0 minutes is 15 feet, and the altitude at 30 minutes is 91 feet. Therefore, the difference in altitude is 91 - 15 = 76 feet.
The difference in time is 30 - 0 = 30 minutes.
Now we can calculate the average rate of change:
Average Rate of Change = Difference in Altitude / Difference in Time
= 76 feet / 30 minutes
≈ 2.53 feet per minute.
Rounded to the nearest whole number, the average rate of change is about 3 feet per minute. Therefore, the correct answer is:
- The rate of change is about 3 feet per minute.