# Calculo

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• Publicado : 23 de agosto de 2010

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Valeria Rebollo Tavera a01062514
Erick Sosa Villagómez a01062495
Sandra Urbina Chavez a01062323
Evelyn Gpe. Galván B. a01062598

Part I – Population Data

In the attached Excel file is data for the population of Mexico from 1895 to 2005. The data is presented as a table and also as a graph.

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On the data sheet of the Excel file are additional columns (blank) for:
∆P (change in population
∆t ( time interval
∆P/∆t ( rate of change of population (“growth rate”)
∆[∆P/∆t]/∆t ( rate of change of growth rate

a)
b) Create formulas in Excel to calculate these quantities for each of the columns.
|Population of Mexico | | | | |
|ineg.gob.mx| | | | | |
| | | | |1st Derivative |2nd Derivative | |
| |# of persons |# of persons |years |units? |units? |(up) or (down) |
|Year |Population |∆P|∆t |∆P/∆t |∆[∆P/∆t]/∆t |Concavity |

1895 |12,700,294 |x |x |x | |x | |1900 |13,607,259 |906,965 |5 |181393 |x |x | |1910 |15,160,369 |1,553,110 |10 |155311 |-2608.2 |down | |1921 |14,334,780 |-825,589 |11 |-75053.54545 |-20942.2314 |down | |1930 |16,552,722 |2,217,942 |9 |246438 |35721.28283 |up | |1940 |19,653,552 |3,100,830 |10 |310083 |6364.5 |up ||1950 |25,791,017 |6,137,465 |10 |613746.5 |30366.35 |up | |1960 |34,923,129 |9,132,112 |10 |913211.2 |29946.47 |up | |1970 |48,225,238 |13,302,109 |10 |1330210.9 |41699.97 |up | |1980 |66,846,833 |18,621,595 |10 |1862159.5 |53194.86 |up | |1990 |81,249,645 |14,402,812 |10 |1440281.2 |-42187.83 |down | |1995 |91,158,290 |9,908,645 |5 |1981729 |108289.56 |up | |2000 |97,483,489 |6,325,199 |5|1265039.8 |-143337.84 |down | |2005 |103,263,388 |5,779,899 |5 |1155979.8 |-21812 |down | |
c) What are the units associated with the population growth rate?
The number of people and the years in which this rate occurred.

d) What are the units associated with the rate-of-change of the growth rate?
Number of people over the number of years, per years.

Part II – Analysis ofPopulation Data

Based on the data that you calculated in Part I:

a) When has the growth rate been positive? When has it been negative? Why do you think the growth rate may have been negative?
In all the years the growth has been positive, except between 1910 and 1921. We think that the growth rate was negative, because Mexico was going through the revolution. And people was fighting andworrying about so many things they didn’t have that much time to have kids. The revolution took the family men away.

b) When was the growth rate increasing? What is the concavity of the graph during these times?
Everyone except in 1921. It is going down.

c) When was the time of greatest growth rate? Do you observe an inflection point on the graph at this time?
At 1995.Yes, it changes the direction and starts going faster positively.

d) When was the growth rate decreasing? What is the concavity of the graph during these times?
1910, 1921, 1990, 2000 and 2005. The concavity starts to be with the curve down.

Population level changes based on the relation between new people entering the population (IN) and existing people leaving the population (OUT).The IN can be births and immigration. The OUT can be death and emigration.

e) What could cause changes in the birth rate?
That the men go to other parts of the world, a war, hunger, also if people are too busy and have too much work like in Japan.

f) What could cause changes in the death rate?
Better health care, medicine, healthier way of living.

g) What could...