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# VB-Question 4

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### VB-Question 4 - Page Text Content

BC: Why is a quadratic function more reasonable for this problem than a linear function would be? A quadratic function is more reasonable for this problem than a linear function because it is a parabola and it is declining down to zero. It hits more points on the line than a linear function would. The water doesn't drain at a constant rate. It drains faster as time goes on. Also, if it were a linear function, the line would continue down into negative and the bathtub can't hold negative liters.

FC: Splish! Splash! I'm Taking A Bath! Question #4 Victoria Binda

1: Question #4: Assume that the number of liters of water remaining in the bathtub varies quadratically with the number of minutes which have elapsed since you pulled the plug. -If the tub 38.4, 21.6, and 9.6 liters remaining at 1,2, and 3 respectively, since you pulled the plug, write an equation expressing liter in terms of time. -How much water was in the tub when you pulled the plug? -When will the tub be empty? -In the real world, the number of liters would never be negative. What is the lowest number of liters the model predicts? Is this number reasonable? -Why is a quadratic function more reasonable for this problem than a linear function would be?

2: If the tub has 38.4, 21.6, and 9.6 liters remaining at 1,2, and 3 respectively, since you pulled the plug, write an equation expressing liters in the terms of time. y=2.4x^2-24x+60 This equation was found by first creating 3 ordered pairs. (1,38.4) (2,21.6) (3,9.6) From here, the data needs to be put into a calculator. On the calculator, press After pressing STAT, a menu will come up. When you press edit, L1 and L2 columns will come up. Enter the minutes, 1,2, and 3, into L1 and enter the liters, 38.4,21.6, and 9.6, into L2. From here, calculate the quadratic regression. It will be in the set up of "ax^2+bx+c" When finding the quadratic regression, it can be viewed as a quadratic function on the graph.

3: How much water was in the tub when you pulled the plug? When the plug was pulled, there was 60 liters in the bathtub. This answer was found by looking at the equation, which expresses liters. The equation is in the setup of ax^2+bx+c. You can find out how much water was in the tub when the plug was pulled by looking at "c." In this equation, c is equal to 60.

4: When will the tub be empty? The tub will be empty when there is 0 liters of water left. There will be 0 liters of water in the tub at 5 minutes. This answer was found by looking at the STAT plot data. L2 is the column for liters in the bathtub.In L2, find where it says 0. In L1, it tells the time. According to data, it takes 5 minutes for there to be 0 liters of water left.

5: In the real world, the number of liters would never be negative. What is the lowest number of liters the model predicts? Is this number reasonable? The lowest number of liters the model predicts is 0. Yes, zero is a reasonable number because the tub is empty at zero. It wouldn't be a negative because once the tub is empty, it is empty. You can't have negative liters of water.

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• By: tori b.
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