Discussion population growth | Mathematics homework help


To examine the enlargement of a population mathematically, we use the concept of interpreterial models. Generally momentous, if we nonproduction to prognosticate the development in the population at a undoubtful bound in era, we set-on-foot by because the exoteric population and use an productive annual enlargement trounce. For illustration, if the U.S. population in 2008 was 301 favorite and the annual enlargement trounce was 0.9%, what would be the population in the year 2050? To work-out this whole, we would use the aftercited formula:

P(1 + r)n

In this formula, P represents the judicious population we are because, r represents the annual enlargement trounce developed as a decimal and n is the enumeobjurgate of years of enlargement. In this illustration, P = 301,000,000, r = 0.9% = 0.009 (recall that you must sever 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 ascertain:

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

Let’s revolve the site where we nonproduction to ascertain out when the population earn embrace. Let’s use this corresponding illustration, but this era we nonproduction to ascertain out when the doubling in population earn happen turgid the corresponding annual enlargement trounce. We’ll set up the whole approve the aftercited:

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

Now, we earn sever twain sides by 301,000,000. This earn concede us the aftercited:

2 = (1.009)n

To work-out for n, we want to challenge a particular interpreter amiables of logarithms. If we conduct the log of twain sides of this equation, we can advance interpreter as shown below:

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

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

n = log 2 / log (1.009)

Using the logarithm character of a calculator, this becomes:

n = log 2/log (1.009) = 77.4

Therefore, the U.S. population should embrace from 301 favorite to 602 favorite in 77.4 years turgid annual enlargement trounce of 0.9 %.

Now it is your turn:

  • Search the Internet and detail the most late population of your abode avow. A amiable assign to set-on-foot is the U.S. Census Bureau (www.census.gov) which maintains all demographic counsel for the province. If potential, settle the annual enlargement trounce for your avow. If you can not settle this appreciate, feel frank to use the corresponding appreciate (0.9%) that we used in our illustration over.
    • Determine the population of your avow 10 years from now.
    • Determine how desire and in what year the population in your avow may embrace turgid a undeviating annual enlargement trounce.
  • Look up the population of the city in which you subsist. If potential, ascertain the annual percentage enlargement trounce of your abode city (use 0.9% if you can not settle this appreciate).
    • Determine the population of your city in 10 years.
    • Determine how desire until the population of your city embraces turgid a undeviating enlargement trounce.
  • Discuss factors that could maybe govern the enlargement trounce of your city and avow.
    • Do you subsist in a city or avow that is experiencing enlargement?
    • Is it potential that you subsist in a city or avow where the population is on the dismiss or hasn’t alterable?
    • How would you work-out this whole if the instance compromised a undeviating dismiss in the population (say -0.9% annually)? Show an illustration.
  • Think of other true earth applications (so monitoring and modeling populations) where interpreterial equations can be utilized.