Calculating and Plotting ln World Population: 1900-1980

In summary, world population is calculated by using census data and statistical models to adjust for births, deaths, and migration. The formula for calculating ln world population is ln(P) = ln(P0) + r(t-t0), and it is used because of its mathematical properties and ability to linearize population growth. Plotting ln world population allows for a clearer understanding of growth rates and trends, and it can be used to predict future population growth but with caution as it may not account for potential changes in factors such as birth rates, mortality rates, and migration patterns.
  • #1
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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  • #2
Looks like a clear assignment to me.
What is the problem?
 

1. How is the world population calculated?

The world population is calculated by taking the total number of individuals living on Earth at a specific time and place, and adjusting for births, deaths, and migration. This is often done using census data and statistical models.

2. What is the formula for calculating ln world population?

The formula for calculating ln world population is ln(P) = ln(P0) + r(t-t0), where P is the current population, P0 is the initial population, r is the growth rate, t is the current time, and t0 is the initial time. This formula is based on the natural logarithm, which is commonly used for modeling population growth.

3. Why is ln used instead of a regular logarithm?

The use of ln instead of a regular logarithm is due to its mathematical properties that make it easier to work with in population models. It is also used because population growth is typically exponential, and the natural logarithm helps to linearize this relationship for easier analysis and visualization.

4. What is the significance of plotting ln world population?

Plotting ln world population allows for a clearer understanding of the growth rate and trends in population over time. It also helps to visualize the exponential nature of population growth and identify any changes in growth patterns.

5. Can ln world population be used to predict future population growth?

Yes, ln world population can be used to make predictions about future population growth based on current trends and growth rates. However, these predictions should be interpreted with caution as they may not account for potential changes in factors such as birth rates, mortality rates, and migration patterns.

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