Lauren Trombetta
Blog Assignment 2
2/9/15
Professor Little
The Change in
Human Population Growth over Time
A)
I choose a data set representing the growth
in human population from 1930-1980 which can be found on this website: http://www.nss.org/settlement/nasa/Contest/Results/2005/TEMIS/Population%20Design.htm
B)
The data set I chose shows the relationship
between time and population growth of the world in millions. Therefore, I pose the
question of what is the exact rate of population growth at the year 1930.
a.
Year 1=1900
b.
Year 2=1910
c.
Year 3=1920
d.
etc
C)
A)
Shown are three ARCS from the year 1930:
a.
From 1930 to 1940
i. (2295-2070)/(5-4)=225/1
b.
From 1930 to 1960
i. (3005-2070)/(7-4)=311.67
c.
From 1930 to 1970
i. (3707-2070)/(8-4)=409.25
As the years increase from 1930 the slopes
get steeper and steeper. Therefore, in
relation to my data, as the year from 1930 increase the population growth gets
more drastic.
G)
Choose a second point (Q) on the tangent
line, and calculate the slope of the line (PQ). This calculation will be the
instantaneous rate of change ((IRC or derivative at a point)…be sure to
identify the units correctly).
Explain what this calculation means mathematically and in terms of your
experiment/application.
First Point: (4,2070)
Second Point: (7.5, 3000)
IRC:
(3000-2070)
/(7.5-4)=900/3.5=257.14
H) I know that 257.14 is the IRC because it is the slope of the
tangent line I made from the focal point of the secant lines from part E. As I
choose years (x values) that got farther away from the year 1930, the slopes
got larger. However the slope at the point 1930, should be less than all of
those points and should approach the secant lines as it does. 257.14 is in fact
smaller than the slopes found in the previous portion of this assignment and
approaches the tangent lines. Therefore the rate of change at exactly 1930 is
257.14/1.
So what?!?!
One can see that because the tangent line’s
slope is smaller than the slopes of the secant lines from the year 1930, the
population of the world is increasing by decade to decade at a higher rate than
the population rate from the year 1930. This would indicate that this is not a
linear function as the slopes are not fairly consistent with on another.
I like the topic you chose, it seems really pertinent to this concept. The graphs are on point too, especially how you illustrated the tangent line.
ReplyDeleteI like how you created your own example. The graphs are really clear and neat. I also like how you included a "so what" in your blog. Good job!
ReplyDeleteI like how you created your own example. The graphs are really clear and neat. I also like how you included a "so what" in your blog. Good job!
ReplyDeletelauren,
ReplyDeletereally nice job! population growth is always an excellent topic to investigate rates of change. your graphs and tables are well done and easy to read! i like how you gave a detailed explanation of your results, showing that you definitely understand the concept of the IRC. additionally, your question matches the rest of your experiment, so that your results make sense.
the only thing that you forgot is the units when calculating your secant lines and your tangent line. other than that, great job!
professor little