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 recorded in the table. Therefore, the domain is {0, 10, 20, 30, 40, 50}.
B. To calculate the average rate of change of the mass of the water between 0 and 50 minutes, we need to find the change in mass and divide it by the change in time.
Change in mass = final mass - initial mass = 525 - 900 = -375 grams
Change in time = final time - initial time = 50 - 0 = 50 minutes
Average rate of change = change in mass / change in time = -375 / 50 = -7.5 grams per minute
The negative sign indicates a decrease in mass over time. In this situation, the average rate of change of the mass of the water represents the rate at which the water is evaporating. Therefore, the average rate of change of -7.5 grams per minute means that the water is evaporating at a rate of 7.5 grams per minute.
C. To determine how long it will take for all of the water to evaporate, we need to find the time when the mass of the water reaches 0 grams. From the given data, the mass of the water decreases by approximately 7.5 grams every minute.
Since the initial mass of the water is 900 grams and the rate of change is -7.5 grams per minute, we can set up an equation to represent the relationship between time (t) and mass (m):
m = 900 - 7.5t
To find the time when the mass reaches 0 grams, we set the equation equal to 0 and solve for t:
0 = 900 - 7.5t
7.5t = 900
t = 900 / 7.5
t = 120 minutes
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