Exponential Growth

Hello,  I have attached a assignment that was not completed.. Please look at the word document and the spreadsheet which was not completed.  I need this completed in a rush before midnight if possible.

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 Population on 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 percentt = 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 x.

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

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EXPONENTIAL GROWTH 1

EXPONENTIAL GROWTH 2

Exponential growth

Donald R Earl

Initial Population = 50 Lion s

Annual growth rate 1= 0.3 percent

Annual growth rate 2=0.5 percent

Annual growth rate 3=0.7 percent

Future population for rate 1

· After 3 years = 122 Lion s

· After 5 years= 224 Lion s

· After seven years =408 Lion s

Future population for rate 2

· after 3 years = 224 Lion s

· after 5 years= 609 Lion s

· 7 years= 1655 Lion s

Future population for rate 3

· after 3 years = 408

· after 5 years= 1655

· 7 years= 6714

Report

This model was specifically meant to find out exponential growth of Lion s in a park. From the model it is apparent that if the current growth rate continues unaltered, the growth will increase exponentially until a certain point, and then it declines. Also, it is clear that the growth rate can be altered and a state of ecological stability is realized. The state of equilibrium can be established so that the main material requirements of each Lion in the park are met.

Increase in yearly population follows a specific pattern which is referred to by mathematicians as exponential growth. Normally, a number shows exponential growth when it increases through a steady percentage of the whole in a continuous time period. Such growth is very rampant in biological systems across the world. From the calculations, it is clear that exponential growth is an occurrence, which indicates that there factors changing with time. When different number of animals is growing in a simultaneous manner in given system and interrelated, a complex way of analyzing future growth and behavior of the system becomes a difficult task. With technology, a new approach of understanding the dynamic aspects of exponential growth in complex environments has been established. This approach is referred to as system dynamics.

The main feature of this approach is the structure of the population. Various relationships among the system are often necessary in deciding the behavior as specific component. It is obvious that the population is dependent on other factors, hence constant interaction. For example, the Lion s’ population is affected significantly by factors such as

· Food

· Capital growth

· Resources

· Pollution

After a certain period of time, each of the above factors also feeds back to have self influence. In this report, the main idea is the wide behavior approaches which will reflect the world systems as it attains the maximum point. This strategy of determining behavior applications is involves prediction in the limited perspective. Since the above approach is only focusing on general approaches, the information is not much detailed. Therefore, one general population is considered. The Lion population reflects the standard global population in a statistical manner.

Exponential growth can be affected by different kinds of pollutants such asbestos, mercury, and lead. A generalized resource that reflects a mixture of non-renewable resources follows a general dynamic procedure at its own rate. This particular level of aggregation is important at this point to make the model easy to understand. Also, it controls the information expected to get from the approach. Actually, with regard to output, it is of o meaning at all. Also, it is of relevance to get an understanding of various causes in the Lion population.

From the graph, the behavior mode of the exponential growth is that of slow but gradual growth. Lion population is expected to increase tremendously at a certain point where there is abundant food and insignificant disturbance from external forces. Other forces expected to play a major role in the growth rate is the encroachment of humans in their habitat. It is evident that all the animals are supposed to be having good relationship with the environment so that the population increases exponentially. It can be concluded from the graph that the park is still experiencing some kind of resource abundance. This is attributed to ever increasing animal population. Also, the interaction between the animals and humans is of significance. Human beings can cause major disruptions to the park and alter the population. However, from the graph, it is quite evident that there are major alterations in the park because there is a still a gradual increase in the size of the population. Human wildlife conflict is another factor that plays a role in exponential growth of the Lion population. Since some of the products such as Lion fur have been found to be of greater value in the market, people can disrupt the growth rate. This can be observed in a slow population increase. Regarding the above model, it can be said that the need for such products may be hamper the rapid growth rate of the population in the park. Even if policies are put in place to monitor and control poaching, it is evident that some human wildlife conflict exists in the park.

The initial population can be used to determine if there is any suspicious activity within the park. For instance, if the animals are reducing in number, exponential growth calculations are used to indicate such changes. In cases where the population after three years is constant, it means that something is wrong within the park and must be investigated. Also, the approach is used by park managers to know if the population is facing any life threatening situations. If the calculations reveals that there is a drastic increase over small period of time, there may be need to cull the population so that they can have access to adequate resources. Competition for food is dangerous and can lead to fighting and killing among the Lions. Therefore, exponential growth rate is an indicator of the kind of growth within the park. This approach offers a sound management strategy and makes sure that a prediction is made.

Talking about predictions, exponential growth rate can enable experts predict future populations effectively. For example, a continuous trend of growth rate like 0.2 per year can provide experts with an opportunity to predict future population. This kind of predictions facilitates management approaches within the park. For example from the calculations, it is clear that future population rates can be easily determined for various rates, that is rate 1, 2, and 3. This offers an effective chance to minimize the population if there is an anticipation of future food or space shortage. On the other hand, population can be allowed to increase drastically in cases where there is potential for enough food and space in the park. As a result, this paves way for effective management strategies and elimination of assumptions by park managers.

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Future Population for Rate 1
Future Population for Rate 2
Future Population for Rate 3

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