MONT 102N – Modeling the Environment Midterm Exam – October 28, 2011

Your Name:

Directions

Do all work on these sheets. You may use the back sides if necessary. There are 100 possible points (distributed as indicated in the questions).

I. In discussing amounts of water needed for irrigation of farmland, a common unit of volume is the acre-foot. One acre-foot of water is the amount of water necessary to cover a flat field one acre in area, to a depth of one foot. Using the tables below, answer questions A and B.

A. (10) How many cubic yards (yd^{3}) of water are in one acre-foot?

B. (10) How many cubic meters (m^{3}) of water are in one acre-foot?

II. The following table gives amounts (in tons) of materials of different types recycled in Washington State in two years, 1986 and 1998.

Category  1986 1998
Paper  391994 821994
Metal  9528 318710
Plastic 349 9871
Glass  48013 113338
Organics + Others 352 903466

A. (20) Construct a pie chart for each year showing how the total recycled materials breaks down into these categories.

B. (10) Based on the pie charts, briefly describe two differences between the two years.

A. (11) In 2002, there were about 4.71×10^{5} alternate fuel vehicles (powered by electricity, ethanol, natural gas, etc.) on the road in the U.S. By 2004, the number had risen to 5.48 × 10^{5}. Construct a linear model for AF V = number of alternate fuel vehicles, as a function of t = years since 2002. What does your model predict about the number AFV in 2011?

B. The following spreadsheet shows a scatterplot for the number of AFV vehicles on the road (in units of 10^{5} vehicles) over a longer time period starting in 1995. Mark the correct responses to the questions below.

1. (3) Based on the scatter plot, the correlation coefficient r is probably: between −1 and −.5 between −.5 and 0 between 0 and .5 between .5 and 1

2. (3) The least squares regression line for this data set would have a slope m about: m = 1/10 m = 1/3 m = 1

3. (3) Which is larger: the average increase per year over the first five years the average increase per year over the last five years Essay (30)

Exactly what does Jared Diamond mean by a “collapse” and what are the five factors he identifies as the major contributors to the collapses he studies. Describe one of those collapses (your choice) in a general way and indicate which of the five factors were involved in that particular case.