Exponential Growth, math homework help

Assignment 1: LASA 2: Exponential Growth

In Module 4, you were introduced to the
concept of exponential functions that can be used to model growth and
decay. Recall what you learned in The Number e lecture. In this
exercise, you will use a Microsoft Excel spreadsheet to calculate the
exponential growth of a population of your choosing. (If you use the
linked spreadsheet below, it is recommended that you consider relatively
small populations and not those of entire nations.)

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 ten years. For example, 10, 20, 30 years would be good
   choices. If you want to see a more dramatic change, select a longer time
   frame such as 10, 50, and 100 years.
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. To draw an
   exponential curve for each series, do the following:
   1. Right click on the middle point for one of the series.
   2. Click on add trendline.
   3. Under Trendline Options, select Exponential.
   4. Click Close
   5. Repeat these steps for the other series.

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.