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Calculus: Final Project
Transcript of Calculus: Final Project
The table below shows the rates for each time interval (in years) after being calculated by using the rate of growth/decay as shown in my last step.
Created by Callan Loflin
Starting in the year 1348 and killing and estimated 75-200 million people, the Black Death was one of the most devastating pandemics in human history. This project will explore the rates at which population increased and decreased at different times. After the rates have been found an approximation will be found of the population had the Black Death not occurred. In addition, the percent of the population of 2000 that would increase without the Black Death will be found too.
How I Started
According to the picture above, I have established that the population is modeled after the equation P(t)=Po x e^rt. In order to solve for rate we will use the time intervals provided by the chart in the previous slide. (i.e. To find the rate of growth from 1200 to 1300 I let the initial population equal 1200. Then t will equal 100 since that is the amount of time that passed between the two given numbers.)
Next....I solved as shown below.
This is the chart given in the original problem.
Now, observing the chart in the last bubble, you will notice there is one that has a negative sign in the time period of 1348 to 1400. This is the indicator of the population drop as a result of the Black Death. So now that part of the assignment has been found and I have laid the groundwork for the next part it is time to find the population had the Black Death not occurred. In order to find the new population, the rates listed in the above table will be used. I will start with the population at 1300 since the Black Death did not affect anything up to this point. My work is shown in the picture above.
By observing my result, this signifies that had the Black Death not occurred and had the population continued to grow at the same rate that it did in the first half of the century then in 1400 the population would have been approximately 591,683,000. I followed the same steps for the remaining time periods and then created another chart displaying my results as pictured below.
Finally, I used the populations in 2000 (the new population without the black death and the original population with the black death). The percent increase = (new population – original population) / original population. Now plugging in the numbers, the percent increase = (9,820,930,000 – 6,200,000,000) / (6,200,000,000). Percent increase = 0.584 or 58.4%. Therefore, if the Black Death would not have taken place there would have been about a 58.4% increase in the population in 2000.
In conclusion, I chose this project because I think studying diseases, epidemiology, and things of that nature are really interesting. Also, I thought it would be interesting to observe and figure out the population rates had the detrimental event, the Black Death, not occurred. Through this final project, I learned several things but I think that the most interesting thing was the alarming rate at which the population is growing and how much of an affect a highly eradicating disease has on a population.
This is me working on the project.