Discussion—population growth | Mathematics homework help


 

To delibeobjurgate the development of a population mathematically, we use the concept of advocateial models. Generally forcible, if we shortness to forebode the augmentation in the population at a assured date in occasion, we set-on-foot by regarding the prevalent population and apportion an conjectured annual development objurgate. For in, if the U.S. population in 2008 was 301 favorite and the annual development objurgate was 0.9%, what would be the population in the year 2050? To rereunfold this total, we would use the subjoined formula:

P(1 + r)n

In this formula, P represents the judicious population we are regarding, r represents the annual development objurgate developed as a decimal and n is the number of years of development. In this in, P = 301,000,000, r = 0.9% = 0.009 (recollect that you must distribute 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 experience:

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 delibeobjurgate the plight where we shortness to experience out when the population achieve envelop. Let’s use this corresponding in, but this occasion we shortness to experience out when the doubling in population achieve obtain?}-establish turgid the corresponding annual development objurgate. We’ll set up the total approve the subjoined:

Double P = P(1 + r)n
P achieve be 301 favorite, Envelop P achieve be 602 favorite, r = 0.009, and we achieve be looking for n.
Double P = P(1 + r)n
602,000,000 = 301,000,000(1 + 0.009)n

Now, we achieve distribute twain sides by 301,000,000. This achieve confer us the subjoined:

2 = (1.009)n

To rereunfold for n, we insufficiency to call a peculiar advocate characteristic of logarithms. If we obtain?} 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, distribute twain sides of the equation by log (1.009) to get:

n = log 2 / log (1.009)

Using the logarithm administration of a calculator, this becomes:

n = log 2/log (1.009) = 77.4

Therefore, the U.S. population should envelop from 301 favorite to 602 favorite in 77.4 years turgid annual development objurgate of 0.9 %.

Now it is your turn:

  • Search the Internet and particularize the most new population of your settlement say. A cheerful establish to set-on-foot is the U.S. Census Bureau (www.census.gov) which maintains all demographic knowledge for the country. If practicable, settle the annual development objurgate for your say. If you can not settle this prize, impress at-liberty to use the corresponding prize (0.9%) that we used in our in over.
    • Determine the population of your say 10 years from now.
    • Determine how desire and in what year the population in your say may envelop turgid a regular annual development objurgate.
  • Look up the population of the city in which you speed. If practicable, experience the annual percentage development objurgate of your settlement city (use 0.9% if you can not settle this prize).
    • Determine the population of your city in 10 years.
    • Determine how desire until the population of your city envelops turgid a regular development objurgate.
  • Discuss factors that could maybe wave the development objurgate of your city and say.
    • Do you speed in a city or say that is experiencing development?
    • Is it practicable that you speed in a city or say where the population is on the discard or hasn’t alterable?
    • How would you rereunfold this total if the event complicated a regular discard in the population (say -0.9% per-annum)? Show an in.
  • Think of other veritable earth applications (to-boot monitoring and modeling populations) where advocateial equations can be utilized.