Andrei has a glass tank that he would like to fill with marbles and water.W(m) models the amount of water Andrei needs (in liters) if he uses m marbles.m103268W(m)36.528.816.2\end{tabular}When does the necessary amount of water decrease faster?Choose 1 answer:(A) Between 10 marbles and 32 marbles(B) Between 32 marbles and 68 marbles(C) The necessary amount of water decreases at the same rate over both intervals
Q. Andrei has a glass tank that he would like to fill with marbles and water.W(m) models the amount of water Andrei needs (in liters) if he uses m marbles.m103268W(m)36.528.816.2\end{tabular}When does the necessary amount of water decrease faster?Choose 1 answer:(A) Between 10 marbles and 32 marbles(B) Between 32 marbles and 68 marbles(C) The necessary amount of water decreases at the same rate over both intervals
Calculate average rate of change: To determine when the necessary amount of water decreases faster, we need to calculate the average rate of change of the water function W(m) over the two intervals: [10,32] and [32,68].
Calculate average rate of change between 10 and 32 marbles: First, we calculate the average rate of change of W(m) between 10 marbles and 32 marbles using the formula: (W(32)−W(10))/(32−10).
Substitute values into formula: Substitute the given values into the formula: (28.8−36.5)/(32−10)=(−7.7)/22=−0.35 (rounded to two decimal places).
Calculate average rate of change between 32 and 68 marbles: Now, we calculate the average rate of change of W(m) between 32 marbles and 68 marbles using the formula: (W(68)−W(32))/(68−32).
Substitute values into formula: Substitute the given values into the formula: (16.2−28.8)/(68−32)=(−12.6)/36=−0.35 (rounded to two decimal places).
Compare average rates of change: Comparing the two average rates of change, we see that they are both −0.35. This means that the necessary amount of water decreases at the same rate over both intervals.
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