A machine is filling a container with candy. The graph below shows the relationship between the amount of candy C (in grams) in the container and the time T (in seconds) since the machine began filling the container.
Amount of candy (grams)
C1002003004005006007008009001000T1234567890
Time (seconds)
(a)Write an equation to represent the relationship between C and T.
(b)Choose the correct statement to represent this relationship.
The machine is filling the container with 100 grams of candy per second.
The machine is filling the container with 1 gram of candy per 100 seconds.
The machine is filling the container with 1 gram of candy per second.
The machine is filling the container with 200 grams of candy per second.
(a) To find an equation to represent the relationship between C and T, we need to determine the pattern in the data. Looking at the graph, we can see that as the time T increases by 1 second, the amount of candy C increases by 100 grams. This tells us that the rate of change is 100 grams per second. We can use this information to write the equation:
C = 100T
(b) The correct statement to represent this relationship is:
The machine is filling the container with 100 grams of candy per second.
(a) To write an equation to represent the relationship between C and T, we can examine the pattern in the graph. We can see that as the time T increases by 1 second, the amount of candy C in the container increases by 100 grams. Therefore, the equation that represents this relationship is: C = 100T.
(b) The correct statement to represent this relationship is: The machine is filling the container with 100 grams of candy per second.
To answer these questions, you need to analyze the graph provided. The graph shows the relationship between the amount of candy (C) in grams and the time (T) in seconds since the machine began filling the container.
(a) To write an equation to represent the relationship between C and T, you can observe the pattern in the graph. Look for any consistent change in C with respect to T. In this case, you can see that for every unit of time that passes (1 second), the amount of candy increases by 100 grams. Therefore, the equation that represents this relationship is:
C = 100T
(b) Now, let's consider the statements given and determine which one correctly represents the relationship.
The machine is filling the container with 100 grams of candy per second.
This statement correctly represents the relationship based on the equation C = 100T. It indicates that for every second (per second), the machine is adding 100 grams of candy to the container.
The machine is filling the container with 1 gram of candy per 100 seconds.
This statement is incorrect because it incorrectly reverses the relationship between candy grams and time. The equation C = 100T shows that 100 grams are added for every second, not for every 100 seconds.
The machine is filling the container with 1 gram of candy per second.
This statement is incorrect because it fails to account for the actual rate of filling. The correct rate is 100 grams per second, not 1 gram per second.
The machine is filling the container with 200 grams of candy per second.
This statement is incorrect because it misinterprets the data. The graph does not indicate that the machine is adding 200 grams per second; rather, it shows a constant rate of 100 grams per second.
Therefore, the correct statement to represent this relationship is: "The machine is filling the container with 100 grams of candy per second."