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Homework Assignment

You are to work alone to analyze and prepare answers/solutions for the following questions and/or case studies. The text should be your primary source of information throughout this course.  

Consolidate your response into one file and submit it to your instructor not later than Sunday Midnight central time. Name your file with your name and the week number, i.e. Jones6 or Brown6.  Your file should be in either Microsoft word (*.doc) or rich text (*.rtf) format.  

Submit your assignment by attaching it into the Dropbox, by clicking on the Dropbox tab at the top of the course frame and choosing the current week assignment. Do not paste it into the Dropbox.

 

Week 6 Assignment

 

You are to prepare answers to the following questions based on the information in the text. Throughout this course, the primary source of information to answer homework questions should be the text book.  Each question has the same point value.

• If you completed the LEAD self instrument, would you be able to assess your leader’s style?  why, or Why not?
• Provide four examples of powerless verbal communication.
• What are the four basic functions of nonverbal cues?  Provide examples of each.
• What are the guidelines that Carl Rogers proposed to perfect the technique of active listening?

if a car accelerates from 5 m/s to 15 m/s in 2 seconds, whats the car’s average acceleration

To study the growth of a population mathematically, we use the concept of exponential models. Generally speaking, if we want to predict the increase in the population at a certain period in time, we start by considering the current population and apply an assumed annual growth rate. For example, if the U.S. population in 2008 was 301 million and the annual growth rate was 0.9%, what would be the population in the year 2050? To solve this problem, we would use the following formula:

P(1 + r)ⁿ

In this formula, P represents the initial population we are considering, r represents the annual growth rate expressed as a decimal and n is the number of years of growth. In this example, P = 301,000,000, r = 0.9% = 0.009 (remember that you must divide by 100 to convert from a percentage to a decimal), and n = 42 (the year 2050 minus the year 2008). Plugging these into the formula, we find:

P(1 + r)ⁿ = 301,000,000(1 + 0.009)⁴²
= 301,000,000(1.009)⁴²
= 301,000,000(1.457)
= 438,557,000

Therefore, the U.S. population is predicted to be 438,557,000 in the year 2050.

Let’s consider the situation where we want to find out when the population will double. Let’s use this same example, but this time we want to find out when the doubling in population will occur assuming the same annual growth rate. We’ll set up the problem like the following:

Double P = P(1 + r)ⁿ
P will be 301 million, Double P will be 602 million, r = 0.009, and we will be looking for n.
Double P = P(1 + r)ⁿ
602,000,000 = 301,000,000(1 + 0.009)n

Now, we will divide both sides by 301,000,000. This will give us the following:

2 = (1.009)ⁿ

To solve for n, we need to invoke a special exponent property of logarithms. If we take the log of both sides of this equation, we can move exponent as shown below:

log 2 = log (1.009)ⁿ
log 2 = n log (1.009)

Now, divide both sides of the equation by log (1.009) to get:

n = log 2 / log (1.009)

Using the logarithm function of a calculator, this becomes:

n = log 2/log (1.009) = 77.4

Therefore, the U.S. population should double from 301 million to 602 million in 77.4 years assuming annual growth rate of 0.9 %.

Now it is your turn:

• Search the Internet and determine the most recent population of your home state. A good place to start is the U.S. Census Bureau (www.census.gov) which maintains all demographic information for the country. If possible, locate the annual growth rate for your state. If you can not locate this value, feel free to use the same value (0.9%) that we used in our example above.
  • Determine the population of your state 10 years from now.
  • Determine how long and in what year the population in your state may double assuming a steady annual growth rate.
• Look up the population of the city in which you live. If possible, find the annual percentage growth rate of your home city (use 0.9% if you can not locate this value).
  • Determine the population of your city in 10 years.
  • Determine how long until the population of your city doubles assuming a steady growth rate.
• Discuss factors that could possibly influence the growth rate of your city and state.
  • Do you live in a city or state that is experiencing growth?
  • Is it possible that you live in a city or state where the population is on the decline or hasn’t changed?
  • How would you solve this problem if the case involved a steady decline in the population (say -0.9% annually)? Show an example.
• Think of other real world applications (besides monitoring and modeling populations) where exponential equations can be utilized.