Mathematical and Technological Literacy I Assignment 2: Exponential Modeling with Percentages

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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.

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)

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:

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?   Show your table.

6.  In 2010, the 2009 populations and projected population rates were released for Russia and Ethiopia.  The population of Russia in 2009 was 140.9 million; the population of Ethiopia was 82.8 million.  Russia is decreasing in population by approximately 0.4% annually; the population of Ethiopia is growing at 2.6%. Using Excel, answer the following questions. 

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

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