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.

****My homestate is Texas and my Hometown is Austin****

Why Work with Us

Top Quality and Well-Researched Papers

We always make sure that writers follow all your instructions precisely. You can choose your academic level: high school, college/university or professional, and we will assign a writer who has a respective degree.

Professional and Experienced Academic Writers

We have a team of professional writers with experience in academic and business writing. Many are native speakers and able to perform any task for which you need help.

Free Unlimited Revisions

If you think we missed something, send your order for a free revision. You have 10 days to submit the order for review after you have received the final document. You can do this yourself after logging into your personal account or by contacting our support.

Prompt Delivery and 100% Money-Back-Guarantee

All papers are always delivered on time. In case we need more time to master your paper, we may contact you regarding the deadline extension. In case you cannot provide us with more time, a 100% refund is guaranteed.

Original & Confidential

We use several writing tools checks to ensure that all documents you receive are free from plagiarism. Our editors carefully review all quotations in the text. We also promise maximum confidentiality in all of our services.

24/7 Customer Support

Our support agents are available 24 hours a day 7 days a week and committed to providing you with the best customer experience. Get in touch whenever you need any assistance.

Try it now!

How it works?

Follow these simple steps to get your paper done

Place your order

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Receive the final file

Once your paper is ready, we will email it to you.

Our Services

No need to work on your paper at night. Sleep tight, we will cover your back. We offer all kinds of writing services.

Essays

No matter what kind of academic paper you need and how urgent you need it, you are welcome to choose your academic level and the type of your paper at an affordable price. We take care of all your paper needs and give a 24/7 customer care support system.

Admissions

Admission Essays & Business Writing Help

An admission essay is an essay or other written statement by a candidate, often a potential student enrolling in a college, university, or graduate school. You can be rest assurred that through our service we will write the best admission essay for you.

Reviews

Editing Support

Our academic writers and editors make the necessary changes to your paper so that it is polished. We also format your document by correctly quoting the sources and creating reference lists in the formats APA, Harvard, MLA, Chicago / Turabian.

Reviews

Revision Support

If you think your paper could be improved, you can request a review. In this case, your paper will be checked by the writer or assigned to an editor. You can use this option as many times as you see fit. This is free because we want you to be completely satisfied with the service offered.