Calculating and Plotting ln World Population: 1900-1980

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SUMMARY

This discussion focuses on calculating the natural logarithm (ln) of world population estimates from 1900 to 1980 and plotting these values against the corresponding years. The population data provided includes key years such as 1900 with 1.6 billion and 1980 with 4.5 billion. Participants are tasked with determining the slope (k) of the best-fit line through these points and evaluating the suitability of an exponential model for this data. Alternative functions are suggested for potentially better fitting the population growth trend.

PREREQUISITES
  • Understanding of logarithmic functions, specifically natural logarithm (ln).
  • Familiarity with linear regression analysis and slope calculation.
  • Proficiency in data visualization tools, such as Matplotlib or Excel.
  • Basic knowledge of population growth models and their mathematical representations.
NEXT STEPS
  • Explore how to use Matplotlib for plotting data in Python.
  • Learn about linear regression techniques and how to calculate the slope of a line.
  • Investigate alternative mathematical models for population growth, such as logistic growth functions.
  • Study the implications of using exponential versus polynomial functions for modeling real-world data.
USEFUL FOR

Data analysts, statisticians, and researchers interested in demographic studies and mathematical modeling of population growth trends will benefit from this discussion.

mualbuq
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For the period from 1900 to 1980, calculate the log base e (ln) of the world population values and plot these values on the vertical axis against the year on the horiontal axis. Draw the best straight line you can through these points and determine its slope, k. What is the exponential equation for this line? Is an exponential a good fit over this 80 year period? If not, what sort of function might do a bit better?

World population estimates in billions of people:
Year World
1650 0.5
1850 1.1
1900 1.6
1910 1.7
1930 2.0
1950 2.5
1960 3.0
1970 3.6
1980 4.5
2000 6.0
 
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Looks like a clear assignment to me.
What is the problem?
 

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