Sung-Hi is filling a sandbox with sand at the rate shown in the table below. Which statement must be true regarding the linear function that represents this situation?
Amount of Sand in the Sandbox
Number of Minutes Since Sung-Hi Started
0
1
2
3
4
Amount of Sand in the Sandbox (pounds)
200
220
240
260
280
The initial value must be 0 pounds.
The initial value must be 20 pounds.
The rate of change must be 0 pounds per minute.
The rate of change must be 20 pounds per minute.
The correct statement is: The initial value must be 200 pounds.
Given the data provided, we can calculate the rate of change by finding the difference in the amount of sand between two consecutive points and dividing it by the difference in the number of minutes.
Let's calculate the rate of change for each consecutive pair of data points:
- Between 0 minutes and 1 minute: (220 pounds - 200 pounds) / (1 minute - 0 minute) = 20 pounds/minute
- Between 1 minute and 2 minutes: (240 pounds - 220 pounds) / (2 minutes - 1 minute) = 20 pounds/minute
- Between 2 minutes and 3 minutes: (260 pounds - 240 pounds) / (3 minutes - 2 minutes) = 20 pounds/minute
- Between 3 minutes and 4 minutes: (280 pounds - 260 pounds) / (4 minutes - 3 minutes) = 20 pounds/minute
As we can see, the rate of change is consistently 20 pounds per minute.
Therefore, the statement "The rate of change must be 20 pounds per minute" must be true regarding the linear function that represents this situation.