Exponential growth (final project) | Mathematics homework help


In Module 4, you were introduced to the concept of exponential functions that can be used to pattern enlargement and consumption. Recall what you versed in The Enumeblame e lecture. In this application, you procure use a Microsoft Excel spreadsheet to investigate the exponential enlargement of a population of your choosing. (If you use the linked spreadsheet underneath, it is recommended that you consider relatively fine populations and not those of complete nations.)

 

Microsoft Excel spreadsheet that you procure use to accomplish the estimations for this

In the spreadsheet, accomplish the aftercited operations:

 

  1. Input a population estimate into the box instant to Initial Population on the spreadsheet. This population should be anything such as the mob, animals, microorganisms, or plants.
  2. Input a blame of enlargement for your population into the box instant to Rate 1. Since we are spirited in a assured annual percent enlargement blame per year, this enumeblame should be elder than cipher percent. Be stable to input this enumeblame in the constitute of a decimal.
  3. Repeat the aloft proceeding for Rate 2 and Rate 3. Gain stable that the estimates you choice dispute by two percent. For pattern, the estimates 0.01, 0.03, and 0.05 would be cheerful choices.
  4. Under the Time (years) column, input three disputeent year estimates. Gain stable that your estimates development by a partiality of ten years. For pattern, 10, 20, 30 years would be cheerful choices. If you omission to see a past melomelodramatic diversify, choice a coveter end shape such as 10, 50, and 100 years.
  5. When you input all of your facts, you’ll see that the spreadsheet has accomplished the estimations for the coming magnitude of each population, blame of enlargement, and end end. Additionally, this knowledge procure be presented graphically in the chart. To sketch an exponential incurvation for each train, do the aftercited:
    1. Right click on the average subject-matter for one of the train.
    2. Click on add trendline.
    3. Under Trendline Options, choice Exponential.
    4. Click Close
    5. Repeat these steps for the other train.

Now that you’ve completed your segregation, it is now end to tidings the results and criticize your findings.

In a Microsoft Word instrument, suit to the aftercited:

  1. Calculate what the coming magnitude of the population procure be, absorbed a favoring judicious population, blame of enlargement, and end end.

Use the exponential equation: Coming estimate = Present estimate * exp(rt)

    • exp is the dishonorable "e"
    • r = annual blame of enlargement explicit as a percent
    • t = years

Note: The spreadsheet accomplished these estimations for you, so you can cohibit the rejoinder you earn after a while those in the spreadsheet. In regulate to accomplish this estimation, you’ll need to enjoy access to a philosophical calculator that procure enjoy an ex dot in regulate to accomplish the exp(rt) estimation. There are a enumeblame of detached philosophical calculators serviceable balance the Internet. Additionally, all smartphones enjoy calculator apps that enjoy a philosophical mode. Cohibit after a while your preceptor for a register of currently serviceable detached options if you do not own a philosophical calculator.

  1. Repeat the estimation for at meanest two other estimates of t; gain stable they are at meanest two years secret from one another. Use the identical estimates you input into the spreadsheet and parallel the rejoinders you earn to those that show in the spreadsheet.
  1. Repeat the estimations using two past choiceions of population enlargement blame; enstable that each population enlargement blame is at meanest two percent disputeent than the others. Use the identical estimates you input into the spreadsheet and parallel the rejoinders you earn to those that show in the spreadsheet.
  1. Examine the graph that your spreadsheet done dishonorabled upon the estimations. Did this graph depend of undeviating lines or incurvationd lines? Describe the fashion of these lines for each enlargement blame. How did they dispute? Why?
  2. Explain the implications of enlargement blame for your population. What do you gard procure bechance balance a covet end of end if a absorbed population of organisms is undisputed to development after a whileout limits? Are there environmental factors that restrain populations from growing exponentially unchecked? What would be the impression on environmental contrivances? 
  3. Explain the presumption of your results. Would it be expected that the percent enlargement blame would cling continuous balance covet ends? Is exponential enlargement an embezzle effrontery for covet ends? If not, what other diversifys in population magnitude jurisdiction be expected?

For this assignment, you procure suggest a spreadsheet and a tidings. The spreadsheet procure be the Microsoft Excel finish containing your segregation. Name your Microsoft Excel finish as follows: LastnameFirstInitial_M5_A1.xls.

The tidings procure be a Microsoft Word instrument in which you procure discourse all of the questions in this assignment in the constitute of a truth. Name your Microsoft Word instrument as follows: LastnameFirstInitial_M5_A1.docx.

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

Assignment 1 Grading Criteria

Maximum Points

Select a population magnitude (population could depend of mob, animals, microorganisms, or plants).

20

Select a assured annual percent enlargement blame per year, which should be elder than 0%.

20

Calculate what the coming magnitude of the population procure be, absorbed the underneath effronterys.

Use the exponential equation:

  • Future estimate = Present estimate *exp(rt)
  • Where exp is the dishonorable “e” of exponential,
  • r = annual blame of enlargement, explicit as a percent
  • t = years

20

Repeat the estimation for SECOND estimate of t (gain stable they are at meanest two years secret from one another).

20

Repeat the estimation for THIRD estimate of t (gain stable they are at meanest two years secret from one another).

20

Graph the results for population enlargement by % enlargement blame, vs. end in years for all FIRST estimations of t.

40

Graph the results for population enlargement by % enlargement blame, vs. end in years for all SECOND estimations of t.

40

Graph the results for population enlargement by % enlargement blame, vs. end in years for all THIRD estimations of t.

40

Explain the implications of this enlargement blame for the population’s contrivance use and the environment.

40

Explain the presumption of your aloft results. 
Would it be expected that the % enlargement blame would cling continuous balance covet ends?

40

Total:

300