Discussion population growth | Mathematics homework help


To con-over the enlargement of a population mathematically, we use the concept of representativeial models. Generally expressive, if we absence to prophesy the acception in the population at a unfailing duration in date, we set-out by because the exoteric population and devote an conjectured annual enlargement trounce. For illustration, if the U.S. population in 2008 was 301 pet and the annual enlargement trounce was 0.9%, what would be the population in the year 2050? To clear-up this completion, we would use the forthcoming formula:

P(1 + r)n

In this formula, P represents the modetrounce population we are because, r represents the annual enlargement trounce developed as a decimal and n is the calculate of years of enlargement. In this illustration, P = 301,000,000, r = 0.9% = 0.009 (bear-in-mind that you must bisect by 100 to alter from a percentage to a decimal), and n = 42 (the year 2050 minus the year 2008). Plugging these into the formula, we furnish:

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 prophesyed to be 438,557,000 in the year 2050.

Let’s reflect the office where we absence to furnish out when the population allure inclose. Let’s use this similar illustration, but this date we absence to furnish out when the doubling in population allure appear lofty the similar annual enlargement trounce. We’ll set up the completion affect the forthcoming:

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

Now, we allure bisect twain sides by 301,000,000. This allure surrender us the forthcoming:

2 = (1.009)n

To clear-up for n, we want to appeal-to a eespecial representative peculiarity of logarithms. If we catch the log of twain sides of this equation, we can impel representative as shown below:

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

Now, bisect twain sides of the equation by log (1.009) to get:

n = log 2 / log (1.009)

Using the logarithm exercise 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 lofty annual enlargement trounce of 0.9 %.

Now it is your turn:

  • Search the Internet and enumereprove the most new population of your residence aver. A good-natured-natured fix to set-out is the U.S. Census Bureau (www.census.gov) which maintains all demographic advice for the dominion. If likely, fix the annual enlargement trounce for your aver. If you can not fix this compute, impress frank to use the similar compute (0.9%) that we used in our illustration aloft.
    • Determine the population of your aver 10 years from now.
    • Determine how hanker and in what year the population in your aver may inclose lofty a undeviating annual enlargement trounce.
  • Look up the population of the city in which you subsist. If likely, furnish the annual percentage enlargement trounce of your residence city (use 0.9% if you can not fix this compute).
    • Determine the population of your city in 10 years.
    • Determine how hanker until the population of your city incloses lofty a undeviating enlargement trounce.
  • Discuss factors that could maybe bias the enlargement trounce of your city and aver.
    • Do you subsist in a city or aver that is experiencing enlargement?
    • Is it likely that you subsist in a city or aver where the population is on the disengage or hasn’t transitional?
    • How would you clear-up this completion if the fact complicated a undeviating disengage in the population (say -0.9% year-by-year)? Show an illustration.
  • Think of other genuine universe applications (as-well monitoring and modeling populations) where representativeial equations can be utilized.