Nouantro is an international producer and seller of
Pianos. They sell different types of
pianos and ship them to different locations in all over the world. Their prices are
determined by the global supply and demand which make their prices fluctuate over different
times. Last year, Nouantro has released a new series of grand pianos
called the GP-04. The sales department head was assigned to present the prices
at which the GP-04 pianos were sold in relation to different months during 2013.
During the presentation, the CEO asked him to identify the change in prices in the month of October, since the global demand for pianos was low during
that month. What was the change in
prince of the GP-04 piano in the month of October?
Price
|
33
|
34
|
33
|
40
|
39
|
45
|
47
|
41
|
31
|
23
|
30
|
34
|
Months
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
·
e.
o
23-31/10-9=-8
o
23-41/10-8=-9
o
23-47/10-7=-8
o
23-45/10-6=-5.5
o
23-39/10-5-=-3.2
o As the secant lines get closer, they are approaching 10 thousands dollars. They are a representation of the rate of change, in this case the change in price, from each months of May, June, July, August and September in relation to the month of October,
o As the secant lines get closer, they are approaching 10 thousands dollars. They are a representation of the rate of change, in this case the change in price, from each months of May, June, July, August and September in relation to the month of October,
· f.
· g.
o
23-31/10-9/=-8. This shows that the price of the
GP-04 piano dropped by 8 thousands dollars from September to October. This
calculation mathematically represent the rate of change or the slope between the points
(9,31) and (10,23)
·
h.
o
The values from part g is the IRC because it represents
the rate of change from the point 9 to the point10 at the tangent line. As I also calculated the slope in part e, we see that values are approaching the point 10 as they are decreasing more and more.
Excellent job, Wasim! First, I'd like to say that I really like the premise and the layout of your problem. It's creative and very pleasing to the eye. It's also very easy to follow. As far as I know, you've done the math right. I think in part G, it would be good to mention that the rate of change you found was the instantaneous one. Try to be specific instead of vague! I was a little confused and had to go back to figure out what part G was. Your explanations made sense, and it was all, for the most part, clear!
ReplyDeleteHi Wasim, I think you have done a great job. I really like your idea, it is very unique. And you've done a great job on explaining the math, they were very clear!
ReplyDeleteGreat job Wasim, I think the idea was great and this was well planned. I can understand the explanation just fine :).
ReplyDeletehi, wasim,
ReplyDeletei am a little partial to appreciating your project, since i am a pianist myself. your secant calculations were done accurately and your graphics add to the understanding of your work. you explained that the rates of change are decreasing over time, however, it would be good to include the units and explain that the IRC value that you obtained means that in october the price of pianos is decreasing at a rate of 8 thousand dollars per month.
all in all, great job!
prof little