Quiz 4

Show all work in a neat and organized fashion. Clearly indicate your answers.

10 points possible.

Label all numeric answers. With models, give a concise explanation of the variables.

Example: Suppose a problem asks for a model, and suppose this is the answer:

Tax = 2538.90 + 540.37t dollars, where t is the number of years since 1989.

To receive full credit, this answer must include all of the following:

(1) the correct model (i.e., Tax = 2538.90 + 540.37t),

(2) the correct label for the output (i.e., ``dollars''), and

(3) the correct explanation of the input variable (i.e., ``where t is the number of years since 1989'').

Example: Here is another correct way to write the same answer.

D = 2538.90 + 540.37x, where D= dollars of tax, and x= number of years since 1989.

(See http://www.census.gov/ipc/www/worldpop.html)

(a) Find an exponential model for the world population. Do not round.

(b) Use the model to predict the world population in 2005.

(c) According to the model, what is the constant yearly percentage change?

2. (5 pts.) At the end of World War I, in the fall of 1918, an influenza epidemic hit the United States Navy. It spread to the Army, to American civilians, and ultimately to the world. It is estimated that by 1920, twenty million people had died from the epidemic. Five hundred fifty thousand of these were Americans-over ten times the number of WWI battle deaths. The tables below give the total numbers of Navy, Army, and civilian deaths due to the epidemic (based on data from A. W. Crosby, Jr., Epidemic and Peace 1918, Westport, Connecticut: Greenwood Press, 1976).

Total Deaths     Total Civilian Deaths    Week ending       Navy       Army        in 45 Major Cities                                                                              August 31       2                              September 7       13       40                       September 14       56       76       68                September 21       292       174       517                September 28       1172       1146       1970                October 5       1823       3590       6528                October 12       2338       9760       17,914                October 19       2670       15,319       37,853                October 26       2820       17,943       58,659                November 2       2919       19,126       73,477                November 9       2990       20,034       81,919                November 16       3047       20,553       86,957                November 23       3104       20,867       90,449                November 30       3137       21,184       93,641

(a) Find a logistic model to fit the set data for civilian deaths. Do not round.

(b) According to the model, what is the limiting value for civilian deaths?