A. The domain of the function representing the data in the table is the set of all possible input values, which in this case is the set of time values (in minutes) for which the mass of water is recorded. So, the domain of the function is {0, 10, 20, 30, 40, 50}.
B. To calculate the average rate of change of the mass of water between 0 and 50 minutes, we need to find the change in mass over the change in time.
Change in mass = Final mass - Initial mass = 525 - 900 = -375
Change in time = Final time - Initial time = 50 - 0 = 50
Average rate of change = Change in mass / Change in time = -375 / 50 = -7.5
The average rate of change of the mass of the water is -7.5 grams per minute. This means that for every minute that passes, on average, the mass of the water decreases by 7.5 grams.
C. To determine how long it will take for all of the water to evaporate, we can look for the point where the mass of water becomes zero. In the given data, the mass of water decreases by a constant rate of 7.5 grams per minute.
Using the average rate of change, we can set up the following equation:
900 - 7.5t = 0
Solving for t:
7.5t = 900
t = 900 / 7.5
t = 120
Therefore, it will take 120 minutes for all of the water to evaporate.
A scientist has a container of pure water. She raises the temperature of the water to its boiling point, then measures the mass of the water. The scientist adds a constant amount of energy to the container so the water will evaporate, and she records the remaining mass of the water every 10 minutes.
Time (minutes) Mass of Water (grams)
0 900
10 822
20 754
30 670
40 597
50 525
A. What is the domain of the function representing the data in the table?
Constructed Response Question
B. Calculate the average rate of change of the mass of the water between 0 and 50 minutes. Show your work and explain what this rate means in this situation.
Constructed Response Question
C. How long will it take for all of the water to evaporate? Show your work or explain your reasoning.
1 answer