Blog # 2

Blog # 2
Asma Aljarbou 
Math-211
2/11/15

a.     Find a real world application OR design your own experimental application relating to rates of change. (in the blog folder you will find plenty of examples to get you started)

I choose to do the relationship of the world population growth rate (%) over time (years).

worldometers.info

b.     Write a narrative or synopsis explaining your application/experiment and include a question. (for example, what is the velocity of the snowball at exactly 2 seconds? Or how can I find the velocity of the baseball at exactly 3 seconds?)

For the growth rate variation over time “years”, I will try to show you how as times goes, the growth rate decrease and I will be using ARC to find the slope of the tangent line. My proper question will be:

·      How can I find growth rate percentage at the year of 2005?

c.      Create a table of values for the data that you have recorded from your application/experiment.

Years, Y	1950	1975	2005	2035	2065	2095
Growth Rate% R, F(y)	1.78	1.77	1.19	0.66	0.29	0.11

d.     Graph the points using the data from your table of values (connect the dots). 

This graph shows the relationship between population growth rate and time in terms of years and I took this graph from the website I used to find my experiment, but I chose some point to make my graph smaller you can see my graph in part F.

e.     Calculate the slope (ARC) of at least three secant lines originating from the same point on your graph to three different points on your graph

To find the slope ARC the original formula state that [ ARC = f(b)-f(a) / b-a ]

I want to know what happen in the year 2005 so I will use the points of (2005, 2095) (2005, 2065) (2005, 2035)

ARC=0.11-1.19/2095-2005= -0.012 %/Yr

ARC=0.29-1.19/2065-2005= -0.015 %/Yr

ARC=0.66-1.19/2035-2005= -0.0176 %/Yr

I notice that as I get closer to point (2005,1.19) the smaller ARC I have, and hopefully I will end up with a limited number very close to the slope of 2005.

f.      Sketch an approximation of a tangent line that passes though the same point (P)

Tangent line at X = 2005 is a line that touches the graph at that point and parallel. As you can see the pink line in the graph represent the tangent line to the function that pass through the point     P= (2005,1.1)

g.     Choose a second point (Q) on the tangent line, and calculate the slope of the line (PQ).

The slope is “rise/run” or “Y2-Y1/X2-X1” and for my point (PQ) P=(2005,1.1), Q=(1975,1.6)

The Instantaneous rate of change IRC = Slope = 1.6-1.1/1975-2005 = - 0.0166 %/Yr

And since my calculations of slope from part d are getting smaller and smaller, this shows that the slope of the secant is getting closer and closer to the tangent line at the point where time = 2005 and if i continue in taking point that closer to X =2005 I will end up having tangent line = secant line.

h.  

my experiment conclude the rise of population growth over the run of years, and In my experiment I was able to find the average population growth rate per year -0.016, and at the year 1950 the secant line has a slope of -0.016. In my experiment in the years of 1950 the population growth rate was in its highest with 1.9% where it is expected to be the lowest with 0.2% in 2095.