Instantaneous Results Blog 2: world population over time Sarah Beiruty

World population over time

b) The world population is increasing over time. The table below shows the number of the world population (in millions) at 10-increment intervals from 1920 till 1980.

Question: what would the population growth exactly be at the year 1950?

c)

The world population growth over Time

Link for results: http://www.vaughns-1-pagers.com/history/world-population-growth.htm

d) Graph

e) From the above graph, I will calculate the slope of  the secant for each of the following intervals. 1950<1980 are (1950,2406) and (1980,4400).

4400-2406 = 66.4

1980-1950

For the interval 1950<1970. Points are (1950,2406) (1970,3700)

3700-2406 = 64.7

1970-1950

For the interval 1950<1960, Points are (1950,2406) and (1960, 2972).

2972-2406 =  56.6

1960-1950

The slope of these secants (the numbers resulted above), are the average rate of change at which the population in the world is changing over the intervals.

The unites for these solutions are million/year.

 f) the tangent line at the point time= 1950 is sketched on the graph above. 

The graph above illustrates how the world population increases over time (years). The slope of the tangent at T=1950 represents the instantaneous rate of change of the population.

g) To find the instantaneous rate of change of the population at 1950 s, I will sketch an approximation of the tangent passing through the point( 1950,2406) and (1943, 2000).

Calculating the slope 2406-2000  = 58

                                    1950-1942

At 58, the number of population is increasing at a rat of approximately 58 million/per year.

h) Therefore we can know that the value of IRC is approximately 58, since if you look at part c, as the secant line gets closer to the slope of the tangent at t=1950, the values are getting closer and closer to 58 starting from 66.4(The last value was 56.6).  Any point resulting on that same line would result with the same slope for the tangent line at the point t=1950.