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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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
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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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xxxxx
xxxxxxxxxxxxxxxx Popluation  xxx  Rate x  xxxx 
xxxx x  xxxx  
Rate x  xxxx  
Time (years)  Future Population xxx Rate 1  xxxxxx xxxxxxxxxx for Rate x  xxxxxx Population xxx xxxx x 
10  352  xxx  xxx 
20  xxx  xxx  709 
30  xxx  581  1059 
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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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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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xxxxxxxxxxx Growth
xxxxxxx’s xxxx
Course
xxxxxxxxxx
Date
Calculate what the xxxxxx size xx xxx population will xxx xxxxx a xxxxxxxx initial population, rate of xxxxxxx and time interval.
xxxxx the xxxxxxxxxxx xxxxxxxx xxxxxxx if xxx initial population xx P, xxxx of growth xx x and time period xx x years xxxx xxx xxxxxxxxxx xxxxx x years would be,
Population x P*
Lets xx calculate xxx rate 1. xxxx r x 0.05, initial population xx 10000.
So, population after 10 xxxxx x xxxxxx x 16487.21
xxxxxx xxx calculation xxx xx xxxxx xxx xxxxx values of t; xxxx xxxx they are xx xxxxx two years apart from one xxxxxxxx Use the xxxx values xxx xxxxx xxxx the spreadsheet and compare the answers you obtain to those that appear xx the spreadsheet.
xxxxx xxx same formula xx above we xxxxx
xxxxxxxxxx xxxxx 30 xxxxx x 10000* = xxxxxxxx
Population xxxxx 60 xxxxx x 10000* x xxxxxxxxx
xxxx xxxx the xxxxxxxxxxx xxx not consider xxx extra decimal xxxxxx xxx xxxxxx the xxxxxxx xxxxxx the answer
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Sheet1
xxxxxxxxxxxxxxxxInitial Popluation  xxxxx  Rate 1  xxxx 
xxxx 2  0.08  
xxxx x  0.01  
xxxx (years)  Future xxxxxxxxxx xxx xxxx x  xxxxxx Population for Rate 2  xxxxxx Population for xxxx x 
xx  16487  xxxxx  xxxxx 
xx  xxxxx  110231  13498 
xx  200855  1215104  18221 
xxxxxx
xxxxxxx
xxxxxxx
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xxxxxxxxxxx Growth
xxxxxxx’s xxxx
xxxxxx
xxxxxxxxxx
xxxx
xxxxxxxxx xxxx the future size xx xxx xxxxxxxxxx will xxx given a specific initial population, xxxx xx growth, xxx xxxx interval.
xxxxx the exponential equation xxxxxxx if the initial population xx P, xxxx of growth xx r and time period xx x years xxxx xxx xxxxxxxxxx xxxxx t years xxxxx be,
xxxxxxxxxx = P*
xxxx xx xxxxxxxxx for xxxx 1. xxxx x x 0.05, xxxxxxx population is 10000.
So, xxxxxxxxxx after 10 years x xxxxxx = xxxxxxxx
xxxxxx xxx xxxxxxxxxxx for xx xxxxx xxx xxxxx values of t; xxxx sure xxxx are xx least two xxxxx apart xxxx xxx another. Use the same values xxx input xxxx the spreadsheet and compare the xxxxxxx xxx obtain to those xxxx xxxxxx in xxx xxxxxxxxxxxx
Using xxx xxxx xxxxxxx as above we have,
xxxxxxxxxx xxxxx 30 xxxxx x 10000* = xxxxxxxx
xxxxxxxxxx after xx xxxxx x 10000* x xxxxxxxxx
xxxx that the spreadsheet did not xxxxxxxx xxx xxxxx xxxxxxx points and xxxxxx xxx xxxxxxx points the answer
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Sheet1
xxxxxxxxxxxxxxxxxxxxInitial xxxxxxxxxx  xxxxx  Rate x  xxxx 
xxxx 2  0.08  
Rate 3  xxxx  
xxxx (years)  Future xxxxxxxxxx xxx Rate 1  Future Population for Rate 2  xxxxxx xxxxxxxxxx for xxxx x 
10  16487  xxxxx  11051 
30  44816  xxxxxx  xxxxx 
xx  200855  1215104  xxxxx 
Sheet1
Sheet2
xSheet3
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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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