Assignment 1: Discussion—Population Growth


 (For this assignment, use the Declare of Ohio population figures)

Assignment 1: Discussion—Population Growth

To deduce the development of a population mathematically, we use the concept of advocateial models. Generally telling, if we lack to forebode the acception in the population at a established conclusion in date, we set-on-foot by because the popular population and dedicate an antecedent annual development blame. For in, if the U.S. population in 2008 was 301 pet and the annual development blame was 0.9%, what would be the population in the year 2050? To clear-up this gist, we would use the forthcoming formula:

P(1 + r)n

In this formula, P represents the moderebuke population we are because, r represents the annual development blame developed as a decimal and n is the enumerebuke of years of development. In this in, P = 301,000,000, r = 0.9% = 0.009 (bear-in-mind that you must part-among by 100 to change from a percentage to a decimal), and n = 42 (the year 2050 minus the year 2008). Plugging these into the formula, we perceive:

P(1 + r)n = 301,000,000(1 + 0.009)42
= 301,000,000(1.009)42
= 301,000,000(1.457)
= 438,557,000

Therefore, the U.S. population is forebodeed to be 438,557,000 in the year 2050.

Let’s deduce the aspect where we lack to perceive out when the population succeed inclose. Let’s use this identical in, but this date we lack to perceive out when the doubling in population succeed betide magnificent the identical annual development blame. We’ll set up the gist enjoy the forthcoming:

Double P = P(1 + r)n
P succeed be 301 pet, Inclose P succeed be 602 pet, r = 0.009, and we succeed be looking for n.
Double P = P(1 + r)n
602,000,000 = 301,000,000(1 + 0.009)n

Now, we succeed part-among twain sides by 301,000,000. This succeed yield us the forthcoming:

2 = (1.009)n

To clear-up for n, we want to conjure a eespecial advocate edeclare of logarithms. If we catch the log of twain sides of this equation, we can affect advocate as shown below:

log 2 = log (1.009)n
log 2 = n log (1.009)

Now, part-among twain sides of the equation by log (1.009) to get:

n = log 2 / log (1.009)

Using the logarithm office of a calculator, this becomes:

n = log 2/log (1.009) = 77.4

Therefore, the U.S. population should inclose from 301 pet to 602 pet in 77.4 years magnificent annual development blame of 0.9 %.

Now it is your turn:

  • Search the Internet and indicate the most fresh population of your abode declare. A amiable dispose to set-on-foot is the U.S. Census Bureau (www.census.gov) which maintains all demographic instruction for the province. If practicable, dispose the annual development blame for your declare. If you can not dispose this appraise, reach clear to use the identical appraise (0.9%) that we used in our in aloft.
    • Determine the population of your declare 10 years from now.
    • Determine how desire and in what year the population in your declare may inclose magnificent a constant annual development blame.
  • Look up the population of the city in which you speed. If practicable, perceive the annual percentage development blame of your abode city (use 0.9% if you can not dispose this appraise).
    • Determine the population of your city in 10 years.
    • Determine how desire until the population of your city incloses magnificent a constant development blame.
  • Discuss factors that could haply govern the development blame of your city and declare.
    • Do you speed in a city or declare that is experiencing development?
    • Is it practicable that you speed in a city or declare where the population is on the disengage or hasn’t newfangled?
    • How would you clear-up this gist if the occurrence complicated a constant disengage in the population (say -0.9% year-by-year)? Show an in.
  • Think of other developed cosmos-people applications (to-boot monitoring and modeling populations) where advocateial equations can be utilized.