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
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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.
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xxx EMBED xxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxx
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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
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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
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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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Exponential Growth
Student’s xxxx
Course
xxxxxxxxxx
Date
Calculate xxxx the xxxxxx size xx xxx population will xxx given x specific xxxxxxx population, rate xx growth, xxx xxxx interval.
Using the exponential xxxxxxxx xxxxxxx if the xxxxxxx population is P, rate xx growth xx r xxx xxxx xxxxxx xx t xxxxx xxxx xxx xxxxxxxxxx after x xxxxx would be,
Population x xx
Lets us calculate xxx rate 1. xxxx x = 0.05, initial population xx xxxxxx
So, xxxxxxxxxx after 10 years x 10000* x xxxxxxxx
xxxxxx xxx calculation xxx at xxxxx xxx xxxxx xxxxxx xx t; make sure they are xx xxxxx xxx years apart from xxx xxxxxxxx Use the xxxx values xxx xxxxx into xxx xxxxxxxxxxx xxx compare the xxxxxxx xxx obtain xx those that xxxxxx xx the spreadsheet.
xxxxx the xxxx xxxxxxx as above xx have,
xxxxxxxxxx after 30 years = 10000* = 44816.89
xxxxxxxxxx xxxxx 60 xxxxx = xxxxxx = 200855.37
Note xxxx the spreadsheet did xxx consider any xxxxx decimal xxxxxx and except xxx xxxxxxx points xxx xxxxxx
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xxxxxx
xxxxxxxxxxxxInitial xxxxxxxxxx  xxxxx  xxxx x  xxxx 
Rate x  xxxx  
xxxx x  0.01  
Time (years)  xxxxxx Population xxx xxxx x  xxxxxx xxxxxxxxxx xxx xxxx 2  xxxxxx Population xxx Rate x 
10  xxxxx  xxxxx  xxxxx 
xx  44816  xxxxxx  13498 
xx  xxxxxx  xxxxxxx  18221 
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xxxxxxx
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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
xxxxxxxxxxxxxxInitial xxxxxxxxxx  xxxxx  xxxx x  0.05 
xxxx x  0.08  
xxxx 3  xxxx  
Time xxxxxxx  Future Population for xxxx 1  Future xxxxxxxxxx for xxxx x  Future Population for Rate 3 
xx  xxxxx  22255  11051 
xx  xxxxx  110231  xxxxx 
60  xxxxxx  xxxxxxx  xxxxx 
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xxxxxx
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