# Math 105--Calculus I: Project 1, Fall 1998

## Caustic rain...

### by Gavin LaRose (glarose@umich.edu), Nebraska Wesleyan University, August 1998

permission granted to use and distribute free in an academic setting.

PostScript version of project

## The letter from the Lonlinc CPE...

### Lonlinc CPE

The Lonlinc Building
South 9th Avenue
Lonlinc, SK 08685

31 August 1998

Independent Mathematical Contractors, Inc.
Lonlinc, SK 04685

Dear IMC:

As you know, the Lonlinc(, Skanebra) Council on the Protection of the Environment (CPE) is charged with the evaluation of all things environmental that may have an impact on the continued health of the residents, animal and human, of the thriving city of Lonlinc. Currently boasting a population of 200,000 and growing at an annual rate of 7%[1], Lonlinc is regarded by some as increasing in size sufficiently fast as to demand appropriate consideration of the environmental impact of such things as the increased traffic attendent with this growth.

One effect of this increase in traffic is an increase of exhaust pollutants in the air, which increase may lead to the phenomenon known as ``acid rain.'' This occurs when NOx from car exhaust combines with atmospheric water to create nitric acid (NO3), rendering any precipitation that might fall acidic. In an effort to determine if this is likely to soon be a problem in the Lonlinc area, we have over the past three years monitored the rate of precipitation and the concentration of NO3 in that precipitation, which data appears in tables 1 and 2 below.

Table 1: Average monthly precipitation (mm)

 month 1 2 3 4 5 6 7 8 9 10 11 12 avg precipitation 17.3 20.6 60 70.5 109.8 114 99.9 98.7 101.6 62.3 35.1 26 month 13 14 15 16 17 18 19 20 21 22 23 24 avg. precipitation 17.7 21.8 59.6 75 110.9 108.8 100.4 102.8 96.5 59.3 36.9 25.5 month 25 26 27 28 29 30 31 32 33 34 35 36 avg. precipitation 17.3 20.9 56.7 13.4 108.9 105.5 92.8 103.3 98.3 60.9 53.9 25.1

Table 2: Average NO3 concentration in precipitation (g/ml)

 month 1 2 3 4 5 6 7 8 9 NO3 conc. 0.4003 0.4033 0.406 0.4078 0.41 0.4124 0.4136 0.4171 0.4184 month 10 11 12 13 14 15 16 17 18 NO3 conc. 0.4214 0.4248 0.4255 0.4282 0.4307 0.4331 0.4356 0.438 0.4409 month 19 20 21 22 23 24 25 26 27 NO3 conc. 0.444 0.4454 0.449 0.4513 0.4532 0.4567 0.4587 0.4603 0.4638 month 28 29 30 31 32 33 34 35 36 NO3 conc. 0.4658 0.47 0.4715 0.4743 0.4772 0.4805 0.4834 0.4852 0.4879

The critical factor in determining the severity of the acid rain is, of course, the amount of NO3 that is deposited on the surfaces on which it falls. We therefore need to establish, based on the data we have collected, how the monthly rate of chemical deposition is changing in time, and to predict when (if ever) this is likely to exceed 11.5g/month on a given 1 cm2 area.

We appreciate your prompt attention to this matter, and look forward to receiving your final report of 3--5 pages on or before the 21st of September. To assure your success in the endeavor, our department's scientific expert, Dr. Gavin LaRose, will be available to answer any questions that you might have in the course of your investigation. He will, however, be unavailable to assist with this project over the weekend of the 18th--20th. You should also plan on meeting with him during the week of the 7th of September to verify your initial progress towards completion of the project. We have made available, through him, a number of sample reports that may prove useful as you develop your formal response.

Sincerely
Jack C. Ousteaux
Director, Lonlinc CPE

jco:glr

[1]: Which has lead some observers to speculate that Lonlinc's population will exceed 1,000,000 by the year 2023!

Gavin's Calc I Project 1, Fall 1998