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EAS 1601
Lab 11:
“Natural Resources and Energy”
Sample Prelab Quiz (note: actual quiz may differ)
1.
Give two examples of renewable resources. (2 pts)
2.
Bauxite (aluminum ore) reserves are currently estimated to be 15,000,000 thousand
tons with a consumption rate of 63,000 thousand tons/year and an annual growth rate
of consumption of 6%.
What is the length of time until depletion of these reserves
assuming exponential growth of consumption? You must show all work (4 pts).
3.
What is carrying capacity?
Name the two types listed in the lab material. (4 pts)
1
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View Full Document EAS 1601
Laboratory 11:
“Introduction to Natural Resources”
Name:
______________________
Section:____________
Background Information
Without an abundance of natural resources, human civilization would not be possible.
Natural resources are necessary for basic human needs such as food and shelter as well as acquired
needs such as transportation, employment/industrial output, entertainment, household lighting,
plumbing and a multitude of other things.
Natural resources can be divided conceptually into two
types,
nonrenewable
and
renewable
resources.
NONRENEWABLE RESOURCES
Nonrenewable resources
exist in finite quantity with respect to the lifetime of human
civilization(s).
Examples of nonrenewable resources are mostly mineral in nature and include
petroleum and coal reserves and mineral resources such as copper, iron, aluminum, and uranium
ore.
In part because of human population growth and in part because more “advanced”
civilizations use more resources per capita, mineral resource usage tends to follow an exponential
growth curve until the resource is significantly depleted.
You can think of it as
firstorder growth
(as opposed to first order loss that is the case in
radionuclide decay) in that consumption is dependent on the quantity/availability of the resource.
The differential equation describing a general first order growth rate is
rL
dt
dL
=
where
t
is time,
L
is the resource consumption rate (change in mineral reserves per unit time) or
resource load
,
r
is the growth rate constant (has units of time
1
).
The firstorder rate equation for
exponential growth can be algebraically rearranged to
rdt
L
dL
=
then integrated with respect to time
∫∫
=
t
L
L
t
t
dt
r
L
dL
00
therefore
()
0
0
ln
t
t
r
L
L
t
−
=
⎥
⎦
⎤
⎢
⎣
⎡
Taking the exponent of both sides of this equation and assuming
t
0
=0
, we can obtain the final
expression:
rt
t
e
L
L
⋅
=
0
where L
t
is the resource load at the observed time t; L
0
is the initial resource load at time t
0
= 0.
For
convenience when working certain problems, the exponential growth equation can be algebraically
rearranged to the following forms solve for
t
or
k
respectively.
rt
L
L
t
=
⎥
⎦
⎤
⎢
⎣
⎡
0
ln
or
rt
L
L
t
=
−
0
ln
ln
It can also be used to obtain an expression for exhaustion time (TEE) of resource R under
exponential growth of load
L
on a given resource.
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This note was uploaded on 02/08/2011 for the course EAS 1601 taught by Professor Lynch during the Spring '08 term at Georgia Institute of Technology.
 Spring '08
 Lynch

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