Homework Assignment Two

Our teacher gave us a class lecture on 4 different types of curves. The 4 types consist of linear, exponential, s-shaped, and plateau curves. He stated that he wanted us to make a prediction of the future using one of these curves to describe that prediction. I believe you could use all 4 curves to describe worldwide human population growth from the past to the present, and even to the future.

Human population growth is a very interesting phenomena. When our ancestors evolved into homo sapiens, their population growth was probably somewhat slow and steady. We did not have advanced technology (e.g. methodical ways to fight predators and prevent disease). If were to look at the our population growth, we would probably see a steady linear curve. Now if we were to compare current human population growth with the past, we would see a jagged curve that would resemble an exponential graph.
Perhaps if were to look into the distant future, we would see a s-shaped curve. A s-shaped curve would be a leveling off of the world's population after a long term exponential growth rate. This could be caused by many different phenomena, such as ozone depletion, the Earth reaching is sustainability limit, nuclear, chemical, or biological warfare, etc. After the S-curve our population would eventually become a plateau curve. This curve would represent a "dying off" of the human race. This could be a result of a series of intricate events (e.g. warming of the earth and a new deadly airborne virus) or the initial cause of the human growth rate leveling off. This is of course speculation, but it seems that the advancement of technology and lack of human discipline has shown us more ways to kill ourselves and put us in harms way.
The majority of things that we affect can also be described by these different graphical representations. For example, the amount of light bulbs in use will decrease or increase proportionally to human population. If you want further evidence for the human race going towards a decline, we must look at the previous extinctions. The Earth has shown us that mass extinctions of species have occurred. For example, many scientists have the popularized the theory that dinosaurs became extinct after an asteroid impelled Earth around Mexico . Regardless of the cause, there is substantial proof from fossils that dinosaurs were wiped off the face of the planet. If you have any doubt about the Earth's previous extinctions, you should read the 6th Extinction by Roger Lewin. This book talks about the patterns of extinction and how we could possibly go through a 6th mass extinction.
Thus, it already clear that human growth rate is growing exponentially, but I believe that our race will eventually die off due to some catastrophic event(s). Many other natural phenomena can be observed by these 4 curves, but I firmly believe that human population growth rate is one of the most applicable.



Our teacher asked us to compute the following:


Estimate the doubling time of the software development productivity of the average programmer, if productivity increases at 6%/year.

The doubling time of the software development would be 12 years. In 12 years any arbitrary amount would double.

Estimate the percent per year of increases in the complexity of PC computers if this complexity doubles every 2 years. (By "complexity" we could say we're talking about the number of transistors on a CPU chip, if you were wondering.)

The approximate percent increase would be 41% per a year. This would give an amount that is very close to 100% of the double any initial arbitrary value.

Estimate the percent per year of increases in the complexity of PC computers if complexity doubles every 18 months, as some think it is doing.

If you have an arbitrary amount of transistors in a PC that have a doubling time of 18 months then you would see a percent increase of approximately 56%.


What is the doubling time of your money if you have it in the bank making 2% interest per year?

It would 35 years for an arbitrary amount of money to double if it is gaining 2% interest.