Assignment 6 Exponential Modeling

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 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? 

4.  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%.  

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? 

5.   Revisit the populations of Russia and Nigeria in question 4 above. 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 these rates, will it take for the population of Nigeria to double? 

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