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# find two consecutive days with both positive and negative values of the river level change

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Whenever the Connecticut River reaches a level of 105 feet above sea level, two Northampton, Massachusetts flood control station operators begin a round the clock river watch. Every two hours they check the height of the river using a scale marked off in tenths of a foot, and record the data in a log book. In the spring of 1996, the flood watch lasted from April 4th, when the river reached 105 feet and was rising at 0.2 foot an hour until April 25th, when the level subsided again to 105 feet. Between those dates their log shows that the river rose and fell several times, at one point coming close to the 115 foot mark. If the river had reached 115 feet, the city would have closed down Mount Tom Road (route 5, south of Northampton).

The graph below shows the rate of change of the level of the river during one portion of the flood watch. Use the graph to answer each question.

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On what date was the river rising most rapidly? How do you know (please explain and show work) ?
On what date was the river falling most rapidly? How do you know (please explain and show work) ?
There were two dates in a row on which the river rose and fell, then rose again during the course of the day. On which days did this occur, and how do you know?
At one minute past midnight, April 14, the river level was 111.0 feet. Estimate its height 24 hours later and 48 hours later. Explain how you made your estimates.
The river crested at 114.4 feet. On what date do you think this occurred and why...explain?

https://brainmass.com/math/calculus-and-analysis/find-two-consecutive-days-with-both-positive-and-negative-values-of-the-river-level-change-361709

#### Solution Summary

River change is contemplated in this solution.

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## Time series and Statistical Control Process: Variables, parameters, linear equation

If the sales, employment, production, and other business series increase or decrease over a period of time and approximate a straight line, the equation for this growth is given by

Y= bX + a, the linear trend equation.

Part 1: State the dependent and independent variables.
Also, state what are the Parameters b & a, and how they are found.

Part 2: In this part assume your independent variable is time, in minute, hours, day, month, or year. Create a time series data knowing that at time zero unit your dependent variable is N and is known. For example at time zero if you statrt boiling the water the water temperature is known and is, say 20 degree C [or use degree F, if you wish]. The dependent variable is the topic of your choice. For example, temperature of water, when you boil it, your water tank level as you fill it out, & so on.

Also, assume that your linear relation is making a 63.5 degree angle with your time-axis, which implies that the relationship has a positive slope of 2.0 [tan (63.5) ~ 2].

Please notice: choose a dependent variable that its variation depends on time. Also assume that the relationship is a linear time dependent relation. Also, note that you have already created an initial point at time zero [i.,e., a point with cordinates of (0, N)]. Your slop is assumed to be positive and equals to 2.

Question is : Please determine your linear equation with the above assumption and predict the first 5 consecutive points on your linear line.

Question 2:

What is statistical process control? How is the concept of statistical process control used in continuous improvement? Discuss with examples.

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