A. Graph B because the slope is at a constant rate B. Graph A because since it is slowly opened the rise of the slope starts of small then rises more C. Graph C since it’s opened a lot the beginning and closed at the end so the rise would start high then go lower as time goes by
A) The graph that best represents the amount of water in the barrel filled by the green hose is graph B. I know this because the green hose is filling the barrel at a constant rate, and graph B shows a constant rate of change, as it's a perfectly straight line increasing.
B) The graph the best represents the amount of water in the barrel filled by the black hose is graph A. This is because the information states that the black hose filled the water at a slow rate at first, since it was slowly being opened, and graph A clearly depicts the rate slowly increasing.
C) The graph that best represents the amount of water in the barrel filled by the blue hose is graph C. I know this because the information states that the blue hose is filling up the barrel normally, but is then slowly closed towards the end. Graph C clearly shows the rate increasing then slowing down.
Remember that the velocity as a function of time is the derivative of the position as a function of time. To solve this we are going to take the derivative of our position function . To do that er are going to apply the power rule of calculus:
We can conclude that the correct answer is:<span>B. V = 24 + 6t - 3t2</span>
. To do that er are going to apply the power rule of calculus: 
