Biz Calc problem help

[Mattyice2]

So for my assignment, my teacher gave us the median values of homes sold in the US from the years 2000 through 2009. We were to input these values onto a graph in excel and create a polynomial trendline to the third degree. Next we were to answer these questions:



1. Find the first and second derivatives of the function that models the trendline.
y=-0.5321x³ + 5.3691x²- 0.3048x + 169.28
y'=-1.5963x² + 10.7382x - 0.3048
y''= -3.1926x + 10.7382
2. Looking at the years from 2000 to 2005, show that the median price for homes was increasing. (Its not showing, but I simply plugged 0-5 in for x on the original equation)
When x=0,

= 169.28
When x=1,

= 173.8122
When x=2,

= 185.89
When x=3,

= 202.3208
When x=4,

= 219.912
When x=5,

= 235.471
When you plug in the year from 2000 to 2005, the median prices are increasing.

3. Find the year in which the median price was increasing at the greatest rate.
The year in which the median price increased at the greatest rate was 2004, from the year 2003.

4. Explain the relationship among your answers for part 1,2, and 3.
The relationship between the questions is that the first derivative is the years during which they were increasing. The derivative of an equation is equal to the slope of any point in the original equation. So you're looking for the time when it was increasing which means the slope is positive. If you're looking for a positive slope then that means you're also looking for when the derivative is positive. On number 2, you are looking for the point at which the median price increased the most. This is the point on the derivative where the slope is most positive or steepest. You do this by taking the second derivative and finding the maximum value within the range you previously found.

5. Provide a possible explanation as to why the median prices began to decrease starting in 2008.
The median prices decreased because the supply of homes exceeded the demand and lead to numerous foreclosures.



So do you guys think that these answers are right? Or do you think he's looking for something different when grading these questions? Particularly numbers 2 and 3. Maybe 4 also.

(The document)

 

[Mattyice2]

So for my assignment, my teacher gave us the median values of homes sold in the US from the years 2000 through 2009. We were to input these values onto a graph in excel and create a polynomial trendline to the third degree. Next we were to answer these questions:


1. Find the first and second derivatives of the function that models the trendline.

y=-0.5321x +5.3691x -0.3048x+169.28
y’=-1.5963x +107382x - 0.3048
y”=-3.1926x +10.7382




2. Looking at the years from 2000 to 2005, show that the median price for homes was increasing.
When x=0, = 169.28
When x=1, = 173.8122
When x=2, = 185.89
When x=3, = 202.3208
When x=4, = 219.912
When x=5, = 235.471
When you plug in the year from 2000 to 2005, the median prices are increasing.


3. Find the year in which the median price was increasing at the greatest rate.
The year in which the median price increased at the greatest rate was 2004, from the year 2003.


4. Explain the relationship among your answers for part 1,2, and 3.
All the three answers have a relationship.The relationship between the questions is that the first derivative is the years during which they were increasing. The derivative of an equation is equal to the slope of any point in the original equation. When we are looking for the time when it was increasing which means the slope is positive. And when you are looking for a positive slope then that means you're also looking for when the derivative is positive. In answer number 2, you are looking for the point at which the median price increased the most. This is the point on the derivative where the slope is most positive or at its peak. You do this by taking the second derivative and finding the maximum value within the range you previously found.


5. Provide a possible explanation as to why the median prices began to decrease starting in 2008.
The median prices decreased because the supply of homes was more than the demand for the same which lead to numerous foreclosures.

Do you think that these answers will be along the lines of what my teacher is looking for?

 

[stapel]

So for my assignment, my teacher gave us the median values of homes sold in the US from the years 2000 through 2009. We were to input these values onto a graph in excel and create a polynomial trendline to the third degree. Next we were to answer these questions:

1. Find the first and second derivatives of the function that models the trendline.

y=-0.5321x +5.3691x -0.3048x+169.28
y’=-1.5963x +107382x - 0.3048
y”=-3.1926x +10.7382

How did you get the first equation? Shouldn't at least some of the variables have powers on them? How did you get the listed derivatives?

2. Looking at the years from 2000 to 2005, show that the median price for homes was increasing.
When x=0, = 169.28
When x=1, = 173.8122
When x=2, = 185.89
When x=3, = 202.3208
When x=4, = 219.912
When x=5, = 235.471
When you plug in the year from 2000 to 2005, the median prices are increasing.

I don't understand this question. Why are you being asked to "show" something when the information (namely, the median prices) is what you were given in the first place? Can't you just point to the list of provided values, and note that each year's value is larger than that of the year before? (By the way, what are you "plugging in" to?)

3. Find the year in which the median price was increasing at the greatest rate.
The year in which the median price increased at the greatest rate was 2004, from the year 2003.

How are you defining "rate" of increase? Are you applying in any manner the information available from the first and second derivatives?

4. Explain the relationship among your answers for part 1,2, and 3.
All the three answers have a relationship.The relationship between the questions is that the first derivative is the years during which they were increasing.

No; the x-values are "the years". It so happens that the values increased in every year. This has no relationship between part (1) and anything else. Instead, you might want to discuss slope (and rate of change) and second derivatives (and max/min points of rates of change, etc).

5. Provide a possible explanation as to why the median prices began to decrease starting in 2008.
The median prices decreased because the supply of homes was more than the demand for the same which lead to numerous foreclosures.

This is neither implied by the mathematics nor supported by the historical facts. You might want to consider reviewing financial news from the period, especially as relates to "housing bubbles", etc, and consider how home values might respond to a rapid deflation of an over-heated market.

I see no way to bring calculus to bear for this part, however.