Discussion—population growth | Mathematics homework help
To con-over the augmentation of a population mathematically, we use the concept of interpreterial models. Generally indicative, if we neglect to foreshadow the extension in the population at a true limit in spell, we set-on-foot by regarding the prevalent population and employ an inconsequent annual augmentation admonish. For stance, if the U.S. population in 2008 was 301 darling and the annual augmentation admonish was 0.9%, what would be the population in the year 2050? To explain this gist, we would use the forthcoming formula:
P(1 + r)n
In this formula, P represents the modeblame population we are regarding, r represents the annual augmentation admonish explicit as a decimal and n is the number of years of augmentation. In this stance, P = 301,000,000, r = 0.9% = 0.009 (retain that you must deal-out by 100 to turn from a percentage to a decimal), and n = 42 (the year 2050 minus the year 2008). Plugging these into the formula, we confront:
P(1 + r)n = 301,000,000(1 + 0.009)42
Therefore, the U.S. population is foreshadowed to be 438,557,000 in the year 2050.
Let’s think the office where we neglect to confront out when the population accomplish enfold. Let’s use this identical stance, but this spell we neglect to confront out when the doubling in population accomplish arise turgid the identical annual augmentation admonish. We’ll set up the gist enjoy the forthcoming:
Double P = P(1 + r)n
P accomplish be 301 darling, Enfold P accomplish be 602 darling, r = 0.009, and we accomplish be looking for n.
Double P = P(1 + r)n
602,000,000 = 301,000,000(1 + 0.009)n
Now, we accomplish deal-out twain sides by 301,000,000. This accomplish produce us the forthcoming:
2 = (1.009)n
To explain for n, we need to call a peculiar interpreter quality of logarithms. If we grasp the log of twain sides of this equation, we can propel interpreter as shown below:
log 2 = log (1.009)n
log 2 = n log (1.009)
Now, deal-out twain sides of the equation by log (1.009) to get:
n = log 2 / log (1.009)
Using the logarithm business of a calculator, this becomes:
n = log 2/log (1.009) = 77.4
Therefore, the U.S. population should enfold from 301 darling to 602 darling in 77.4 years turgid annual augmentation admonish of 0.9 %.
Now it is your turn:
- Search the Internet and recite the most late population of your settlement recite. A amiable settle to set-on-foot is the U.S. Census Bureau (www.census.gov) which maintains all demographic counsel for the say. If practicable, fix the annual augmentation admonish for your recite. If you can not fix this prize, move munificent to use the identical prize (0.9%) that we used in our stance over.
- Determine the population of your recite 10 years from now.
- Determine how crave and in what year the population in your recite may enfold turgid a undeviating annual augmentation admonish.
- Look up the population of the city in which you feed. If practicable, confront the annual percentage augmentation admonish of your settlement city (use 0.9% if you can not fix this prize).
- Determine the population of your city in 10 years.
- Determine how crave until the population of your city enfolds turgid a undeviating augmentation admonish.
- Discuss factors that could haply swing the augmentation admonish of your city and recite.
- Do you feed in a city or recite that is experiencing augmentation?
- Is it practicable that you feed in a city or recite where the population is on the dismiss or hasn’t alterable?
- How would you explain this gist if the contingency concerned a undeviating dismiss in the population (say -0.9% per-annum)? Show an stance.
- Think of other genuine universe applications (too monitoring and modeling populations) where interpreterial equations can be utilized.