Exponential growth (final project) | Mathematics homework help


In Module 4, you were introduced to the concept of exponential functions that can be used to mould augmentation and decadence. Recall what you knowing in The Enumereprimand e lecture. In this training, you conciliate use a Microsoft Excel spreadsheet to apportion the exponential augmentation of a population of your choosing. (If you use the linked spreadsheet adown, it is recommended that you consider proportionately paltry populations and not those of total nations.)

 

Microsoft Excel spreadsheet that you conciliate use to accomplish the reckonings for this

In the spreadsheet, accomplish the aftercited operations:

 

  1. Input a population treaindisputable into the box direct to Initial Population on the spreadsheet. This population should be anything such as the inhabitants, animals, microorganisms, or plants.
  2. Input a admonish of augmentation for your population into the box direct to Rate 1. Since we are assiduous in a unequivocal annual percent augmentation admonish per year, this enumereprimand should be superior than cipher percent. Be indisputable to input this enumereprimand in the contrive of a decimal.
  3. Repeat the aloft proceeding for Rate 2 and Rate 3. Produce indisputable that the treasures you excellent dispute by two percent. For sample, the treasures 0.01, 0.03, and 0.05 would be amiable-natured-natured choices.
  4. Under the Time (years) column, input three disputeent year treasures. Produce indisputable that your treasures enlargement by a restriction of ten years. For sample, 10, 20, 30 years would be amiable-natured-natured choices. If you absence to see a past meretricious qualify, excellent a desireer opportunity mould such as 10, 50, and 100 years.
  5. When you input all of your postulates, you’ll see that the spreadsheet has accomplished the reckonings for the forthcoming largeness of each population, admonish of augmentation, and opportunity interim. Additionally, this counsel conciliate be presented graphically in the chart. To haul an exponential incurvation for each succession, do the aftercited:
    1. Right click on the average apex for one of the succession.
    2. Click on add trendline.
    3. Under Trendline Options, excellent Exponential.
    4. Click Close
    5. Repeat these steps for the other succession.

Now that you’ve completed your decomposition, it is now opportunity to recital the results and study your findings.

In a Microsoft Word muniment, corcorrespond to the aftercited:

  1. Calculate what the forthcoming largeness of the population conciliate be, loving a peculiar orderrebuke population, admonish of augmentation, and opportunity interim.

Use the exponential equation: Forthcoming treaindisputable = Present treaindisputable * exp(rt)

    • exp is the disesteemed "e"
    • r = annual admonish of augmentation developed as a percent
    • t = years

Note: The spreadsheet accomplished these reckonings for you, so you can arrive the rejoinder you earn delay those in the spreadsheet. In arrange to accomplish this reckoning, you’ll deficiency to possess path to a or-laws calculator that conciliate possess an ex molehill in arrange to accomplish the exp(rt) reckoning. There are a enumereprimand of detached or-laws calculators helpful balance the Internet. Additionally, all smartphones possess calculator apps that possess a or-laws order. Arrive delay your professor for a inventory of currently helpful detached options if you do not own a or-laws calculator.

  1. Repeat the reckoning for at lowest two other treasures of t; produce indisputable they are at lowest two years secret from one another. Use the identical treasures you input into the spreadsheet and assimilate the rejoinders you earn to those that show in the spreadsheet.
  1. Repeat the reckonings using two past excellentions of population augmentation admonish; enindisputable that each population augmentation admonish is at lowest two percent disputeent than the others. Use the identical treasures you input into the spreadsheet and assimilate the rejoinders you earn to those that show in the spreadsheet.
  1. Examine the graph that your spreadsheet performed disesteemedd upon the reckonings. Did this graph hold of unswerving lines or incurvationd lines? Describe the construct of these lines for each augmentation admonish. How did they dispute? Why?
  2. Explain the implications of augmentation admonish for your population. What do you opine conciliate occur balance a desire conclusion of opportunity if a loving population of organisms is recognized to enlargement delayout limits? Are there environmental factors that observe populations from growing exponentially unchecked? What would be the collision on environmental instrument? 
  3. Explain the presence of your results. Would it be expected that the percent augmentation admonish would arrive invariable balance desire conclusions? Is exponential augmentation an misspend effrontery for desire conclusions? If not, what other qualifys in population largeness authority be expected?

For this assignment, you conciliate resign a spreadsheet and a recital. The spreadsheet conciliate be the Microsoft Excel rasp containing your decomposition. Name your Microsoft Excel rasp as follows: LastnameFirstInitial_M5_A1.xls.

The recital conciliate be a Microsoft Word muniment in which you conciliate address all of the questions in this assignment in the contrive of a fact. Name your Microsoft Word muniment as follows: LastnameFirstInitial_M5_A1.docx.

Submit twain muniments to the M5: Assignment 1 Dropbox by Monday, July 20, 2015.

Assignment 1 Grading Criteria

Maximum Points

Select a population largeness (population could hold of inhabitants, animals, microorganisms, or plants).

20

Select a unequivocal annual percent augmentation admonish per year, which should be superior than 0%.

20

Calculate what the forthcoming largeness of the population conciliate be, loving the adown effronterys.

Use the exponential equation:

  • Future treaindisputable = Present treaindisputable *exp(rt)
  • Where exp is the disesteemed “e” of exponential,
  • r = annual admonish of augmentation, developed as a percent
  • t = years

20

Repeat the reckoning for SECOND treaindisputable of t (produce indisputable they are at lowest two years secret from one another).

20

Repeat the reckoning for THIRD treaindisputable of t (produce indisputable they are at lowest two years secret from one another).

20

Graph the results for population augmentation by % augmentation admonish, vs. opportunity in years for all FIRST reckonings of t.

40

Graph the results for population augmentation by % augmentation admonish, vs. opportunity in years for all SECOND reckonings of t.

40

Graph the results for population augmentation by % augmentation admonish, vs. opportunity in years for all THIRD reckonings of t.

40

Explain the implications of this augmentation admonish for the population’s productions use and the environment.

40

Explain the presence of your aloft results. 
Would it be expected that the % augmentation admonish would arrive invariable balance desire conclusions?

40

Total:

300