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:
 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.
 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.
 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.
 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.
 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:
 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.
 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.
 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.
 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?
 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?
 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:

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

MAT 106 Module 5 Unit 5 Assignment 1 LASA 2 Exponential Growth(NEW COURSE)A++++WORD+EXCEL is Attached
body preview (0 words)
file1.doc preview (154 words)
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
xxxxxxxxxxxxxxxxxxxInitial Popluation  50  xxxx x  xxxx 
xxxx 2  0.03  
xxxx x  0.05  
xxxx (years)  Future Population xxx xxxx 1  xxxxxx Population for xxxx x  Future xxxxxxxxxx xxx xxxx x 
10  xx  xx  82 
12  56  71  xx 
15  58  78  105 
xxxxxx
xxxxxx
xSheet3
file3.xls preview (23 words)
xxxxxx
xxxxxxxxxxxxInitial xxxxxxxxxx  50  Rate 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  55  67  82 
12  56  xx  91 
15  xx  xx  xxx 
xxxxxx
xSheet2
Sheet3
Buy this answer  Try it before you buy it 
Answer rating (rated one time)
Assignment 1: Exponential Growth
body preview (3 words)
Assignment 1: xxxxxxxxxxx Growth
file1.doc preview (1070 words)
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
   more text follows   
Try it before you buy it 
A++ PERFECTLY DONE (MS EXCEL + WORD REPORT)
body preview (0 words)
file1.docx preview (663 words)
xxxxxxxxxxx Growth
xxxxxxx’s xxxx
xxxxxx
xxxxxxxxxx
xxxx
xxxxxxxxx what xxx xxxxxx xxxx of xxx population xxxx xxx xxxxx x specific xxxxxxx population, rate xx growth, and time interval.
xxxxx the exponential xxxxxxxx formula xx the initial population is xx rate xx xxxxxx is x and time xxxxxx is t xxxxx then the xxxxxxxxxx xxxxx x xxxxx xxxxx xxx
Population = P*
xxxx us calculate for xxxx 1. Here x = 0.05, xxxxxxx xxxxxxxxxx is xxxxxx
So, xxxxxxxxxx after 10 years x xxxxxx = xxxxxxxx
Repeat the xxxxxxxxxxx for at xxxxx two xxxxx xxxxxx of t; xxxx sure xxxx are xx xxxxx xxx years xxxxx from one xxxxxxxx Use the same values you xxxxx xxxx xxx spreadsheet and xxxxxxx the answers xxx obtain to those xxxx appear in xxx xxxxxxxxxxxx
Using xxx xxxx formula as above we have,
Population after xx years = xxxxxx = 44816.89
xxxxxxxxxx after 60 xxxxx = xxxxxx = xxxxxxxxx
xxxx that the spreadsheet did not consider xxx extra xxxxxxx xxxxxx and except xxx decimal points the answer
   more text follows   
file2.xls preview (35 words)
Sheet1
xxxxxxxxxxxxxxxInitial xxxxxxxxxx  10000  xxxx x  0.05 
Rate 2  xxxx  
Rate 3  xxxx  
xxxx xxxxxxx  Future xxxxxxxxxx for Rate 1  Future xxxxxxxxxx for Rate x  xxxxxx Population xxx Rate x 
10  16487  22255  xxxxx 
30  44816  110231  13498 
60  200855  1215104  xxxxx 
xxxxxx
xxxxxxx
xSheet3
xTry it before you buy it 
A++ PERFECTLY DONE (MS EXCEL + WORD REPORT)
body preview (0 words)
file1.docx preview (663 words)
xxxxxxxxxxx Growth
xxxxxxx’s xxxx
xxxxxx
xxxxxxxxxx
xxxx
xxxxxxxxx what xxx future xxxx xx xxx xxxxxxxxxx will xxx xxxxx a specific xxxxxxx population, xxxx of growth, xxx xxxx xxxxxxxxx
Using xxx xxxxxxxxxxx equation formula if xxx initial xxxxxxxxxx xx xx rate of growth xx r xxx time period xx t xxxxx then the xxxxxxxxxx after t xxxxx would be,
xxxxxxxxxx = P*
xxxx us calculate xxx rate xx xxxx x x xxxxx xxxxxxx xxxxxxxxxx xx xxxxxx
xxx population after 10 years x 10000* = xxxxxxxx
Repeat xxx xxxxxxxxxxx for xx least xxx xxxxx values xx t; make xxxx they xxx at xxxxx xxx years xxxxx from one another. Use xxx xxxx xxxxxx you xxxxx into xxx spreadsheet xxx compare xxx xxxxxxx xxx obtain xx those that appear in xxx spreadsheet.
Using the same xxxxxxx xx xxxxx we have,
Population xxxxx xx xxxxx = xxxxxx x 44816.89
xxxxxxxxxx after 60 years x 10000* x 200855.37
xxxx xxxx the xxxxxxxxxxx did not xxxxxxxx any xxxxx xxxxxxx xxxxxx and xxxxxx xxx decimal xxxxxx xxx xxxxxx
   more text follows   
file2.xls preview (35 words)
Sheet1
xxxxxxxxxxxxxxxxxx Popluation  10000  xxxx 1  xxxx 
Rate 2  0.08  
Rate 3  0.01  
xxxx xxxxxxx  xxxxxx Population xxx xxxx x  xxxxxx xxxxxxxxxx xxx xxxx x  Future xxxxxxxxxx for xxxx x 
xx  xxxxx  xxxxx  11051 
xx  44816  xxxxxx  xxxxx 
60  xxxxxx  1215104  xxxxx 
Sheet1
xxxxxx
xxxxxx
Try it before you buy it 