Emie is recording her test grades based on the number of hours she spent studying for each test. The table shows the time she spent studying and the test grade she earned.
Hours Spent Studying | Test Grade
0 | 34
2 | 50
4 | 66
6 | 82
8 | 98
What was the average rate of change of the test grade as the amount of hours she spent studying went from 0 hours to 8 hours?
A. 8
B. 16
C. 4
D. 34
(f(8)-f(0))/(8-0) = (98-34)/8 = 8
To find the average rate of change of the test grade as the amount of hours spent studying went from 0 hours to 8 hours, we can use the formula:
Average rate of change = (Change in test grade) / (Change in hours spent studying)
The change in test grade is 98 - 34 = 64.
The change in hours spent studying is 8 - 0 = 8.
Plugging these values into the formula:
Average rate of change = 64 / 8 = 8
Therefore, the average rate of change of the test grade is 8.
Therefore, the correct answer is A. 8.
To find the average rate of change of the test grade, we need to calculate the difference in the test grade divided by the difference in the number of hours spent studying.
Let's calculate the rate of change between each pair of consecutive points:
- Between 0 hours and 2 hours, the test grade increased by 50 - 34 = 16.
- Between 2 hours and 4 hours, the test grade increased by 66 - 50 = 16.
- Between 4 hours and 6 hours, the test grade increased by 82 - 66 = 16.
- Between 6 hours and 8 hours, the test grade increased by 98 - 82 = 16.
Now, let's calculate the average rate of change by summing up the rate of change between each pair of consecutive points and dividing it by the number of intervals (which is 4):
(16 + 16 + 16 + 16) / 4 = 64 / 4 = 16
Therefore, the average rate of change of the test grade as the amount of hours she spent studying went from 0 hours to 8 hours is 16.
So, the correct answer is B. 16.