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Assignment 1: Exponential Growth

Assignment 1: Exponential Growth

In Module 4, you were introduced to the concept of exponential functions that can be used to model growth and decay. In this exercise, you will use a Microsoft Excel spreadsheet to calculate the exponential growth of a population of your choosing.

Click here to open the Microsoft Excel spreadsheet that you will use to perform the calculations for this assignment.

In the spreadsheet, perform the following operations:

  1. Input a population value into the box next to Initial Populationon the spreadsheet. This population should be anything such as the people, animals, microorganisms, or plants.
  2. Input a rate of growth for your population into the box next to Rate 1. Since we are interested in a positive annual percent growth rate per year, this number should be greater than zero percent. Be sure to input this number in the form of a decimal.
  3. Repeat the above procedure for Rate 2 and Rate 3. Make sure that the values you select differ by two percent. For example, the values 0.01, 0.03, and 0.05 would be good choices.
  4. Under the Time (years)column, input three different year values. Make sure that your values increase by a minimum of two years. For example, 3, 5, 7 years would be good choices.
  5. When you input all of your data, you’ll see that the spreadsheet has performed the calculations for the future size of each population, rate of growth, and time interval. Additionally, this information will be presented graphically in the chart.

Now that you’ve completed your analysis, it is now time to report the results and examine your findings.

In a Microsoft Word document, respond to the following:

  1. Calculate what the future size of the population will be, given a specific initial population, rate of growth, and time interval.

Use the exponential equation: Future value = Present value * exp(rt)

    • exp is the base "e"
    • r = annual rate of growth expressed as a percent
    • t = years

Note: The spreadsheet performed these calculations for you, so you can check the answer you obtain with those in the spreadsheet. In order to perform this calculation, you’ll need to have access to a scientific calculator that will have an ex button in order to perform the exp(rt) calculation. There are a number of free scientific calculators available over the Internet. Additionally, all smartphones have calculator apps that have a scientific mode. Check with your instructor for a list of currently available free options if you do not own a scientific calculator.

  1. Repeat the calculation for at least two other values of t; make sure they are at least two years apart from one another. Use the same values you input into the spreadsheet and compare the answers you obtain to those that appear in the spreadsheet.
  1. Repeat the calculations using two more selections of population growth rate; ensure that each population growth rate is at least two percent different than the others. Use the same values you input into the spreadsheet and compare the answers you obtain to those that appear in the spreadsheet.
  1. Examine the graph that your spreadsheet produced based upon the calculations. Did this graph consist of straight lines or curved lines? Describe the shape of these lines for each growth rate. How did they differ? Why?
  2. Explain the implications of growth rate for your population. What do you think will happen over a long period of time if a given population of organisms is allowed to increase without limits? Are there environmental factors that keep populations from growing exponentially unchecked? What would be the impact on environmental resources?
  3. Explain the likelihood of your results. Would it be expected that the percent growth rate would stay constant over long periods? Is exponential growth an appropriate assumption for long periods? If not, what other changes in population size might be expected?

For this assignment, you will submit a spreadsheet and a report. The spreadsheet will be the Microsoft Excel file containing your analysis. Name your Microsoft Excel file as follows: LastnameFirstInitial_M5_A1.xls.

The report will be a Microsoft Word document in which you will address all of the questions in this assignment in the form of a narrative. Name your Microsoft Word document as follows: LastnameFirstInitial_M5_A1.docx.

Submit both documents to the M5: Assignment 1 Dropbox by Saturday, April 20, 2013.

Assignment 1 Grading Criteria
Maximum Points
Select a population size (population could consist of people, animals, microorganisms, or plants).
20
Select a positive annual percent growth rate per year, which should be greater than 0%.
20

Calculate what the future size of the population will be, given the below assumptions.

Use the exponential equation:

  • Future value = Present value *exp(rt)
  • Where exp is the base “e” of exponential,
  • r = annual rate of growth, expressed as a percent
  • t = years
20
Repeat the calculation for SECOND value of t (make sure they are at least two years apart from one another).
20
Repeat the calculation for THIRD value of t (make sure they are at least two years apart from one another).
20
Graph the results for population growth by % growth rate, vs. time in years for all FIRST calculations of t.
40
Graph the results for population growth by % growth rate, vs. time in years for all SECOND calculations of t.
40
Graph the results for population growth by % growth rate, vs. time in years for all THIRD calculations of t.
40
Explain the implications of this growth rate for the population’s resource use and the environment.
40
Explain the likelihood of your above results.

Would it be expected that the % growth rate would stay constant over long periods?
40
Total:
300
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Answer
Submitted by Google on Thu, 2015-07-02 19:00
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MAT 106 Module 5 Unit 5 Assignment 1 LASA 2 Exponential Growth(NEW COURSE)A++++WORD+EXCEL is Attached

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xxxxxxxxxx future xxxxxxxxxx xxx xx individuals xx xxxxx xx xxxxxxx x xxxxxxxxx Over xxx 20, and 30 years. xxxxx xx

2.

xxx xxxxx rate changes xx 7, x xxx 15 xxxxxxx

xxxx xxxxx rates at the xx year intervals the xxxxx are xxxxxxx xxxxxxxx the xxxx intervals to just the five year xxxx it produces stighter lines, xxx xxxxxxxxxx the rate to xx x and 15 perecent also produces straight lines.

Yes completely the exponential rate gain that xxxx populaion xxxxxxxxxxx just starting off from x xxxxx xx 50 can xxxx but not to xxx xxxxx xx enviromental xxxxx xxxx seem to xx xx xx xxxxxxx speed xxx the intial start xxxxxxxxx But xxxxxxxxx factors xxxxx happen xxxx as loss xx food xxxxxxxxx and xxxx xxxx available to xxxxxxxx

For xxxxx first thirty xxxxx the xxxxxx xxx xx xxxxxx xxx xx xxx xxxxxxxxxx grows the xxxxxx or xxxx xxxx xxxxxxxxx much to xxx xxxxxx xx compounding.

� xxxxx opendocument.CalcDocument.1 ���

xxx EMBED opendocument.CalcDocument.1 ���

xxx EMBED xxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxx

xxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxx

_187392428.unknown

file2.xls preview (23 words)

xxxxxx

xxxxxxxxxxxxxxxxxxx
Initial Popluation50xxxx x xxxx
xxxx 20.03
xxxx x0.05
xxxx (years) Future Population xxx xxxx 1 xxxxxx Population for xxxx xFuture xxxxxxxxxx xxx xxxx x
10 xxxx 82
125671xx
1558 78105

xxxxxx

xxxxxx

x

Sheet3

file3.xls preview (23 words)

xxxxxx

xxxxxxxxxxxx
Initial xxxxxxxxxx50Rate 1 0.01
Rate x xxxx
Rate 3 0.05
Time (years)xxxxxx xxxxxxxxxx xxx Rate 1 Future Population for xxxx x Future xxxxxxxxxx for Rate 3
10 556782
12 56 xx 91
15xx xxxxx

xxxxxx

x

Sheet2

Sheet3


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Answer
Submitted by MathematicsEx... on Sat, 2015-08-29 13:31
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Complete Solution (Text & EXCEL), A+ Grade Guaranteed

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Kindly give x rating xx xx solution and xxx xx know xxxxxxxx you xxxx xxxx in future. xxxxx You.

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xxxxxxxxxxx xxxxxx

According xx recent xxxxxxxxxx the xxxxxx States population is about 319 Million.

Let xx xxxxxxxx xxx xxxxxx growth xxxxx xxx xxxx xxxxxxxxxx xx be 1%, 2% and xx respectively.

The xxxxxx value for xxxx population can be calculated xxxxx the xxxxxxxxx xxxxxxxx

Future xxxxxxxxxx xxxxx 10 years

xxxxxxx Population = 319

xxxxxx xxxx of xxxxxxx x = 1%

xxxx xxxxxxxx x = xx

xxx xxxxxx size of the population, xxxxxxxxxxx xxx xxxxx xxxxxxx xxxxxxxxxxx xxxx of growth, and xxxx interval can be calculated as xxxxxxxx

xxxxx xxx xx initial xxxxxxxxxx of 319 million growing xx an annual rate of 1%, xxx xxxxxx size xx xxx population xxxxx x span xx 10 xxxxx shall be xxxxx xxxxxxxx

Future xxxxxxxxxx xxxxx xx years

xxxxxxx xxxxxxxxxx = 319

xxxxxx rate of xxxxxxx x x 1%

Time (years), x = 20

xxx xxxxxx xxxx xx the population, considering the xxxxx initial xxxxxxxxxxx rate xx growth, xxx xxxx xxxxxxxx can xx calculated xx xxxxxxxx

xx

Thus, xxx an xxxxxxx

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file2.xlsx preview (20 words)

xxxxx

xxxxxxxxx
xxxxxxx Popluation xxxRate xxxxx
xxxx xxxxx
Rate xxxxx
Time (years) Future Population xxx Rate 1 xxxxxx xxxxxxxxxx for Rate xxxxxxx Population xxx xxxx x
10 352 xxx xxx
20xxx xxx 709
30xxx 581 1059


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Answer
Submitted by smartwriter on Fri, 2013-04-12 11:15
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Assignment 1: Exponential Growth

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Assignment 1: xxxxxxxxxxx Growth

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EXPONENTIAL xxxxxx xxx xxxx \* MERGEFORMAT �1� EXPONENTIAL xxxxxx � xxxx xx MERGEFORMAT �3�

Exponential xxxxxxx

xxxxxx

xxxxxxxx

College:

xxxxxxx

Date:

xxxxxxx xxxxxxxxxx = 50 Lion s

Annual xxxxxx rate xx 0.3 xxxxxxxx

Annual xxxxxx xxxx xxxxx percent

xxxxxx xxxxxx xxxx xxxxx percent

Future population xxx xxxx x

After x years = 122 xxxx x

After x xxxxxx xxx xxxx x

After xxxxx years xxxx xxxx s

Future xxxxxxxxxx for rate x

xxxxx 3 xxxxx = 224 xxxx s

after 5 years= 609 Lion s

7 xxxxxx 1655 xxxx x

xxxxxx xxxxxxxxxx xxx rate 3

xxxxx x years = xxxx

xxxxx 5 xxxxxx 1655

7 xxxxxx xxxxx

xxxxxx

This xxxxx xxx specifically meant to xxxx out exponential xxxxxx of Lion s in x park. From xxx xxxxx it is xxxxxxxx that xx xxx current growth rate xxxxxxxxx xxxxxxxxxx the xxxxxx xxxx xxxxxxxx exponentially xxxxx a certain point, and xxxx it declines. xxxxx xx xx xxxxx xxxx xxx growth rate xxx be xxxxxxx and a xxxxx xx ecological xxxxxxxxx is realized. xxx state of xxxxxxxxxxx xxx be xxxxxxxxxxx xx xxxx the main xxxxxxxx requirements of xxxx xxxx in the park are met.

Increase in xxxxxx population xxxxxxx a xxxxxxxx pattern xxxxx is xxxxxxxx xx xx xxxxxxxxxxxxxx xx exponential xxxxxxx xxxxxxxxx x number shows exponential growth when it

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Submitted by schoolbench on Fri, 2016-06-10 10:35
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(EXCEL + DOCUMENT) THIS HAS BEEN GRADED A+++ USE AS A GUIDE

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xxxxxx see xxxxxxxx file xxx xxxxxxx xxxx by x student. xxxxxxx are accurate but use xxxx xx x xxxxx

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xxxxxxxxxxxx Report.docx

I picked xx initial xxxxxxxxxx xx 123,456 xx use xx this investigation. x then used the exponential xxxxxxxxx xxxxxx value x xxxxxxx xxxxxxxxxx x ert xx calculate xxx final xxxxxxxxxx xxxxx x given xxxxxx xx xxxxx In this equation, e xx xxx xxxxxxx number xxxxxxxxxxxxxx xxxxxxxx r is xxx annual xxxx of xxxxxx xxxxxxxxx xx x decimal; xxx x xx xxxx xxxxxx passed xx years.

I xxxx calculated the population xxxxx xx xxxxx using xxxxx xxxxxxxxx growth rates – 5%, xxx and xxx

Population at First xxxx = xxxxxxx xxxxxxxxxx * ert

xxx xxxx x x xxxxxx x e(0.05 * xxx = xxxxxxxxxx xxxxxxxxx with value xxxx spreadsheet xx xxxxxxxxxx Rate 2 = 123456 x xxxxxx * 15) = xxxxxxxxxx confirmed with value xxxx xxxxxxxxxxx xx 352794

xxx Rate x x 123456 * xxxxxx x xxx =476222.33, confirmed xxxx xxxxx from xxxxxxxxxxx of 476222

x xxxxxxxx the process xx find the population xxxxx 30 years.

xxxxxxxxxx at xxxxxx Time x Initial Population x xxx

For xxxx 1 = xxxxxx x xxxxxx x xxx x 553291.41, xxxxxxxxx with xxxxx xxxx spreadsheet of x xxxxxx

xxx Rate x x 123456 * xxxxxx * xxx = xxxxxxxxxxx confirmed with value xxxx xxxxxxxxxxx of x 1008162

For Rate 3 x xxxxxx x e(0.09 x xxx x 1836992.16, xxxxxxxxx with xxxxx from spreadsheet of x xxxxxxx

And I did the xxxx xxxxx xxx xxxxx 45 years.

Population at Third Time x Initial Population * ert

xxx Rate 1 = xxxxxx x xxxxxx x xxx = xxxxxxxxxxx xxxxxxxxx with value xxxx xxxxxxxxxxx xx = 1171317

For Rate 2 x xxxxxx x

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Submitted by Engineer Maxw... on Wed, 2015-02-11 16:09
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A++ PERFECTLY DONE (MS EXCEL + WORD REPORT)

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xxxxxxxxxxx xxxxxx

Student’x Name

xxxxxx

xxxxxxxxxx

xxxx

Calculate what the future xxxx of xxx population will be, xxxxx a xxxxxxxx initial xxxxxxxxxxx xxxx xx growth, and time interval.

xxxxx the xxxxxxxxxxx xxxxxxxx formula if xxx initial population xx P, rate xx growth is r and xxxx xxxxxx is t xxxxx xxxx the xxxxxxxxxx xxxxx t xxxxx would be,

xxxxxxxxxx x P*

xxxx xx xxxxxxxxx for xxxx xx Here r = xxxxx xxxxxxx population xx xxxxxx

So, population after xx years = xxxxxx x 16487.21

xxxxxx xxx calculation xxx at least xxx other xxxxxx of t; make xxxx they are at least xxx xxxxx xxxxx from xxx another. xxx the xxxx xxxxxx xxx xxxxx xxxx the spreadsheet xxx compare xxx xxxxxxx xxx obtain xx xxxxx xxxx appear xx xxx spreadsheet.

xxxxx xxx xxxx xxxxxxx xx above we xxxxx

Population xxxxx 30 years x xxxxxx x 44816.89

Population xxxxx xx xxxxx x xxxxxx = 200855.37

xxxx xxxx xxx xxxxxxxxxxx did xxx consider any xxxxx xxxxxxx points and xxxxxx the decimal points the answer

- - - more text follows - - -

file2.xls preview (35 words)

Sheet1

xxxxxxxxxxxxx
Initial xxxxxxxxxx xxxxxRate 1 xxxx
Rate 2 0.08
xxxx x 0.01
Time xxxxxxxFuture xxxxxxxxxx xxx xxxx xFuture xxxxxxxxxx for xxxx 2 xxxxxx Population for Rate x
xxxxxxx xxxxx xxxxx
30xxxxxxxxxxxxxxxx
xx2008551215104 xxxxx

Sheet1

x
Future xxxxxxxxxx for xxxx 1
xxxxxx xxxxxxxxxx for xxxx 2
Future xxxxxxxxxx xxx xxxx 3

xxxxxx

xxxxxx


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Submitted by Engineer Maxw... on Wed, 2015-02-11 16:09
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A++ PERFECTLY DONE (MS EXCEL + WORD REPORT)

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xxxxxxxxxxx xxxxxx

Student’x Name

xxxxxx

Instructor

Date

xxxxxxxxx what xxx xxxxxx size xx the population xxxx xxx given a specific initial xxxxxxxxxxx rate of growth, and xxxx xxxxxxxxx

Using the xxxxxxxxxxx equation xxxxxxx if the xxxxxxx population xx P, xxxx of xxxxxx xx x and time xxxxxx xx t xxxxx xxxx the xxxxxxxxxx after t years would be,

xxxxxxxxxx x xx

Lets us xxxxxxxxx xxx rate 1. Here r x xxxxx initial population is xxxxxx

So, population xxxxx 10 years x 10000* x 16487.21

Repeat the calculation xxx xx least xxx other xxxxxx xx xx make sure they are at xxxxx two years apart from one another. xxx xxx xxxx values you xxxxx into xxx xxxxxxxxxxx and xxxxxxx xxx answers you obtain to xxxxx xxxx appear in the xxxxxxxxxxxx

xxxxx the same xxxxxxx as above we xxxxx

xxxxxxxxxx xxxxx 30 years x xxxxxx x xxxxxxxx

Population xxxxx 60 years = 10000* = xxxxxxxxx

xxxx that xxx spreadsheet did xxx xxxxxxxx any xxxxx xxxxxxx xxxxxx and except xxx decimal xxxxxx xxx xxxxxx

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xxxxxx

xxxxxxxxxxxxxx
Initial xxxxxxxxxxxxxxxxxxx x0.05
xxxx x 0.08
xxxx 3xxxx
Time xxxxxxx Future Population for xxxx 1Future xxxxxxxxxx for xxxx x Future Population for Rate 3
xx xxxxx 2225511051
xxxxxxx 110231 xxxxx
60xxxxxx xxxxxxx xxxxx

Sheet1

Future xxxxxxxxxx for xxxx x
Future Population for Rate x
xxxxxx xxxxxxxxxx xxx Rate x

xxxxxx

x

Sheet3

x


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Submitted by Good_Morning on Wed, 2015-10-28 08:22
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Assignment 1 LASA 2 Exponential Growth*****Already A++ Rated Tutorial Use as Guide Paper*****

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xxxxxxxxxx x LASA x Exponential Growth

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Assignment x LASA 2 Exponential Growth/Final Report.docx

I xxxxxx xx xxxxxxx xxxxxxxxxx xx 123,456 to xxx xx xxxx xxxxxxxxxxxxxx x xxxx used the exponential xxxxxxxxx xxxxxx value = xxxxxxx Population * ert to xxxxxxxxx the final xxxxxxxxxx xxxxx x xxxxx xxxxxx xx time. In this xxxxxxxxx e is xxx xxxxxxx xxxxxx (approximately xxxxxxxx r xx xxx annual xxxx xx growth expressed xx a decimal; xxx x xx time xxxxxx passed xx years.

I then xxxxxxxxxx the xxxxxxxxxx xxxxx 15 years xxxxx three xxxxxxxxx growth rates – xxx xxx xxx 9%.

Population xx First Time = Initial xxxxxxxxxx * ert

For xxxx 1 = 123456 x e(0.05 x xxx = xxxxxxxxxx xxxxxxxxx xxxx value from spreadsheet xx xxxxxxxxxx xxxx 2 = 123456 x e(0.07 * 15) = xxxxxxxxxx confirmed with xxxxx from spreadsheet of xxxxxx

For xxxx x = xxxxxx x e(0.09 x xxx =476222.33, xxxxxxxxx xxxx xxxxx from xxxxxxxxxxx of 476222

I repeated the process xx xxxx the xxxxxxxxxx after 30 years.

xxxxxxxxxx xx Second xxxx x xxxxxxx Population * xxx

For xxxx 1 x xxxxxx * xxxxxx * 30) x xxxxxxxxxx confirmed with value xxxx xxxxxxxxxxx xx = xxxxxx

For Rate 2 x xxxxxx * xxxxxx * 30) x xxxxxxxxxxx confirmed with xxxxx xxxx xxxxxxxxxxx of = xxxxxxx

For Rate x x xxxxxx x xxxxxx x xxx x xxxxxxxxxxx xxxxxxxxx xxxx value from spreadsheet of x 1836992

And x xxx the same thing xxx xxxxx 45 years.

xxxxxxxxxx xx Third Time = Initial xxxxxxxxxx * ert

xxx xxxx 1 = xxxxxx x xxxxxx x 45) x 1171317.92, confirmed with value from spreadsheet of x

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