Operating instructions

Lifetime of a Non-Renewable
Resource
One of the great problems facing the world today is the
conservation of resources, particularly those which can
not be readily renewed. The simple program
is a good
model of an interactive BASIC simulation.
Marvin L. DeJong
Dept.
of Math & Physics
The School
of the Ozarks
Point Lookout,
MO 25726
Table 1: Resource Depletion Program
1~ PRINT "THIS IS A PllOOllAH TO CAIm!.ATE HOW LOm A NON-RE1lEWABLE
RE30URCE WILL LAST."
2~ PRINT "nPE IN THE ESTIMATED llE>ERVES OF THE RE5OURCE."
3~ PRINT "RESERVES-";
4~ INPUT R
5¢ PRINT "nPE IN THE ANNUAL RATE AT WHICH THE RESOURCE IS CONSUMED."
6¢ PRINT "CONSUMPTION RATEo";
7¢ INPUT C
6¢ PRINT "nPE IN THE ANNUAL PERCENT INCREASE IN THE CONSUMPTION RATE."
9¢ PRIN'l' "GROWTH RATE OF CONSUMPTION·";
1¢¢ INPUT G
11¢ G-G/l¢¢
12¢ Y=¢
13~ R~R-C
14~ C~C+C"G
15¢ Y~Y+l
16~ IF R >¢ TIIPll 13¢
17¢ PRINT "YOUR RESOURCE WILL LAS'!"'; Y; "YEARS."
16¢ Em
Are you interested in doing something
simple, serious, and
of educational
value with your computer? Estimating
the lifetime
of a non-renewable resource
such as coal, oil, or natural gas is often
a
difficult calculation involving calculus
and the use of exponential or
logarithmic functions. The computer
makes it short and super simple, as you
will see. The results have serious impli·
cations.
An editorial in our local paper
claimed
that we have enough coal to last
for centuries. This
mayor may not be
true.
Read on.
Suppose there are R tons
of coal still
unmined. Also suppose that we use C
tons
of coal per year. At the end of one
year
we will have R - C tons left. The
next year we subtract C tons again, and
so on until our coal is gone.
If we kept
track
of the number of subtractions, we
would know how many years the coal
would last. This is the lifetime
of the
resource.
However, we must take
into account
that, typically, the production and con·
sumption
of resources increases over
time. Our demand for electrical power,
fuel oil, natural gas, and gasoline grows.
The gross national product, or GNP, in-
creases in a healthy
(?) economy.
Growth implies increases in
the con-
sumption
of resources, and this must be
taken into account when calculating the
lifetime of a resource.
Assume that consumption of a
resource grows by G percent per year.
If
C tons of coal are consumed this year,
then next year we will consume C tons
of
coal plus the increase, which is G/100
multiplied times C. Anyone who has
calculated interest compounded annual-
January, 1980
Iy knows how
to do the arithmetic. A sim-
ple example may help.
If we use 500
million tons of coal this year, and our
growth rate in the consumption
of coal
is
10 per cent per year, then next year we
will consume 500 million tons plus 10 per
cent
of 500 million tons.
MICRO
-- The 6502 Journal
The calculation
of the lifetime of a
resource is much the same as outlined
above, except that C increases by G per-
cent each year
if the growth factor is
taken into account. A flowchart of the
entire process is shown in Figure
1, and
20:21