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Assignment 2
Exponential Modeling with Percentages

1. a.  A ticket to the Lovehammers concert at Metro was marked up by 95.5%.  If the original price was $10, what was the final price including fees (the marked up price)?

b.  On August 16, 2005, one share of Telephone & Data Systems Inc. stock cost $42.90.  On September 2, 2005, the stock closed 5% lower than the price on August 16th.  What was the cost of one share of Telephone & Data Systems Inc. stock on September 2nd?

2.  The burning of fossil fuels (oil, coal, natural gas) releases carbon dioxide into the atmosphere.  Carbon dioxide is known as a greenhouse gas because it tends to trap heat in the atmosphere, causing global warming.  In 1995, the United States emitted about 1.4 billion tons of carbon (as carbon dioxide) into the atmosphere. China was second largest contributor, emitting 850 million tons.  US emissions were increasing at 1.3% a year, while Chinese emissions were increasing at 4% a year. Assuming these growth rates continued determine the year when China will exceed US in carbon emissions.

3.  In order to understand the prehistory of the Hawaiian island of Lana'i better, anthropologists Maria Sweeney, Melinda Allen, and  Boyd Dixon used radiocarbon dating on charcoal found in an ancient dwelling site, the Kaunolu Village National Historic Landmark, the largest archeological complex on the island.  In one of their samples, they found that approximately 94% of the original carbon 14 remained.  Using the fact that Carbon 14 decays by 1.202% every 100 years, determine the approximate age of the this sample .  In your word document, paste the Excel table you made to come up with your answer.

Lana'i.jpg (21996 bytes)
Hulopoe Beach on Lana'i

Copyright 1998 B. David Cathell, Phoenix, AZ

 

Relative/Percentage Change

                        Relative Change =  =

For communication purposes, we convert relative change, which is a fraction (converted to a decimal number) to a percentage (percentage change).  The following are three ways to convert a fraction (decimal number) to a percentage: 

 For this course, we will generally show percentages formatted to two (2) decimal places (unless stated otherwise).

4.  Chicken Bacteria:  The information given below was found on the label of a package of Chicken.

Bacteria Count on Chicken
(per square centimeter when refrigerated at 40º F)

Day Bacteria Condition
0 360 OK
1 5,760 OK
2 92,160 Fair
3 1,474,560 Poor
4 23,592,960 Odor
5 377,487,360 Slime

 

a.  By using the percentage change formula above, show that the above data is exponential.  What is the percentage increase in bacteria each day?

b.  It is also noted on the label that at 40º F, the bacteria double in number every 6 hours.  Make a new table showing the bacteria count every 6 hours.  To get you started, you table should look like this:

Hour Bacteria
0 360
6  
12  
18  
24  
30  

You should continue your hours column to 120 hours.  Paste your Excel table in your word document.

c.  What is the percentage increase in bacteria every six hours?

5. In 1980, the number of African elephants was 1,200,000 but that number was decreasing 5.25% a year. 

a. How many African elephants were there in 1988?  Show either your table or your calculation.

b. How many years did it take for the population to reach 1/2 of what it was originally?  Use logs and round answer to the nearest tenth.

6.  In 2005, the 2004 populations and projected population rates were released for Russia and Nigeria.  The population of the Russia in 2004 was 143.8 million; the population of Nigeria was 129 million.  Russia is decreasing in population by approximately 0.7% annually; the population of Nigeria is growing at 2.4%.   Using logs and letting x be the number of years since 2004, answer the following questions.  Round both answers to the nearest tenth.

a.  How long, at the above rates, will it take for the population of Nigeria to double? 

b.  How long, at the above rates, will it take for the population of Russia to reach 125 million?