Math Blogpost #2
Ana Maria Lopez
Car depreciation
a.
Car
depreciation
b.
In the real
world, when you buy a car at price X, each year that goes by the price of that
same car decreases. In this example, the owner bought the car for $22,000 and
then ten years later ends up with a car that its worth $4,050. Even though the
car looses value of $17,950 over a period of 10 years, the price did not
depreciate by the same amount each year. So, what is the depreciation rate in
year 5?
c.
|
Time (years)
|
Value (in dollars)
|
|
0
|
22,000
|
|
1
|
16,200
|
|
2
|
14,350
|
|
3
|
11,760
|
|
4
|
8,980
|
|
5
|
7,820
|
|
6
|
6,950
|
|
7
|
6,270
|
|
8
|
5,060
|
|
9
|
4,380
|
|
10
|
4,050
|
d.
Explanation
|
Question #
|
Explanation
|
|
e.
|
For this portion, I
calculated three different secant lines. I wanted to find the IRC for point a
(x=5). Therefore I labeled points a1 (4,8980), a2 (3,11760), and a3 (2,14350) . I drew a secant line from
point a to all three points (a1, a2, a3 ).
In this case a3 is the point
that is furthest away from point a. I found that the slope between these two
points was – 3/6530. I found that as the point got closer to point a ( in
this case point a1 is the closest), the slope became larger (
-1/1160). This connects back to my question since the closest to the actual
depreciation rate in year 5 or x=5 is point a1 where the rate is
-1/1160.
|
|
g.
|
For this section, I drew
a tangent line that passes through point x= 5. In this case I took two points
A and B and found the slope between them. This gave me the IRC or the slope/
derivative at point x=5. The INC I got was -3/6530. I found it interesting
that this number is the same slope I got for the secant line a3 . In
terms of my experiment it means that my depreciation rate at x=5 is
approximately -3/6530 according to the tangent line experiment.
|
|
h.
|
In this case, as the
secant lines approached the value x=5, the numbers got bigger. Therefore the slope of the secant is
becoming closer to the tangent line. By definition, any points in the tangent
line will have the same slope or derivative than the point being analyzed (in
this case x=5). Therefore, when finding the slope
|
This is great, I can see the real world application for having this data, car dealers can use it to try and set their inventory.
ReplyDeleteThis is a great blog entry! The graphs are very clear and the way you presented your work in general is easy to read and easy to understand. Nice job!
ReplyDeleteLove that you used cars as the focus of your blog post! Very well done as well
ReplyDeleteana,
ReplyDeleteyour intro was perfect! i like how you explained why it is important to use the IRC because of the fact that the depreciation value does not move by the same amount every year. kudos!
your graphs and tables look great, however, you calculated the secant and tangent lines backwards. you used the x-values for the numerator and the y-values for the denominator. you can still kind of glean a sense of logic from your results, but they are not entirely accurate since the calculations are reversed. additionally, remember to include the units in both your secant and tangent line calculations.
overall, good job, though. =]
professor little