Essentials of Ecology

SUPPLEMENT 2 S5

2. Which one of the curves in Figure 2
   most closely resembles the upper curve
   in Figure 5? What, if anything, might
   stop that curve from becoming nearly
   vertical?
   It is important to know that line graphs can
   give different impressions of data, depending on
   how they are designed. Changing the measure-
   ment ranges on either of the x- or y-axes can
   change the shape of the curve, and two curves

will end up with $1,024,000. Figure 5 shows the

difference between these two types of growth.

Questions

1. How do you think the upper curve would
   differ if the exponential growth rate were
   1% instead of 10%? How would it differ if
   the rate were 50%? Explain why any expo-
   nential growth curve eventually becomes
   nearly vertical.

Questions

1. Which of the energy sources has seen the
   least growth in consumption through 2007?
   Which two sources are projected to have
   the sharpest growth after 2020? Coal and
   hydropower are both used mostly to gener-
   ate electricity. The U.S. consumed about
   how many times as much coal as hydro-
   power in 2007?


2. Compare Figures 2 and 3. Has the U.S. in-
   creased its use of coal and natural gas more
   sharply or less sharply than the world as a
   whole?
   Figure 4 compares two variables—monthly
   temperature and precipitation (rain and snow-
   fall) during a typical year in a temperate decidu-
   ous forest. However, in this case, the variables
   are measured on two different scales, so there
   are two y-axes. The y-axis on the left end of the
   graph shows a Centigrade temperature scale,
   while the y-axis on the right shows the range
   of precipitation measurements in millimeters.
   The x-axis displays the fi rst letters of each of the
   12 month names.

Questions

1. In what month does most precipitation fall?
   What is the driest month of the year? What
   is the hottest month?


2. If the temperature curve were almost flat,
   running throughout the year at about its
   highest point of about 30 °C, how do you
   think this forest would be different from what
   it is? (See Figure 7-15, p. 154.) If the annual
   precipitation suddenly dropped and remained
   under 25 centimeters all year, what do you
   think would eventually happen to this forest?
   Line graphs can also show dramatic differ-
   ences between two types of the same phenom-
   enon, such as growth. Linear growth is growth
   by a given amount in each interval. Exponential
   growth is growth by a fi xed percentage of a
   growing amount in each interval. For example,
   if you save $1,000 per year under your mattress
   for 70 years, you will end up with $70,000. But
   if you invest $1,000 per year and earn 10% in-
   terest on your total amount invested every year,
   and if you keep it all invested for 70 years, you

Energy consumption

(quadrillion Btu)

Year

History Projected

1985 1990 1995 2000 2005 2010 2015 2020 2025 2030

0

10

20

30

40

50

60

1980

Oil

Coal

Natural gas

Nuclear

Nonhydro renewables

Hydropower

Figure 3 Energy

consumption by fuel

in the United States,

1980–2007, with pro-

jected consumption to

2030. (Data from U.S.
      Energy Information
      Administration/Annual
      Energy Outlook 2007)

350

300

250

200

150

100

50

0

30

20

10

0

–10

–20

–30

–40

Mean monthly temperature (

°C)

Mean monthly precipitation (mm)

Temperate deciduous forest

Freezing point

Month

J F MAM J J A S ON D

Figure 4 Climate graph showing typical

variations in annual temperature (red) and

precipitation (blue) in a temperate decidu-

ous forest.

Thousands of dollars

Year

10

750

1,000

1,250

0 10 20

Exponential growth

($1,000 invested at 10%

per year interest)

$1,024,000

$70,000

30 40 50 60 70

Linear growth

(saving $1,000

per year)

Figure 5 Linear and exponential

growth. If resource use, economic

growth, or money invested grows

exponentially for 70 years at 10%,

it will increase 1,024-fold.