INTRODUCTION
The amount of radiation absorbed by an individual in a given geographical area like Nigeria over the years, have not been fully predicted or estimated. This is because, of the limitation posed by the inability to properly evaluate the average time spent indoor or outdoor per day by people living either in urban or rural areas. Researches show that people engaging in outdoors activities have a higher percentage of radiation absorption, but the estimated radiations absorbed from the atmosphere per day have not been fully achieved (Glowaik and Pacyna, 1980).
In this study, attempt is made to estimate the average time spent outdoor/indoor, in other to properly estimate the amount of outdoor radiation (solar, ionizing and nonionizing) absorbed per day; which will in turn help to determine the amount of dose absorbed at any given time. The need to determine the average time spent for radiation absorption and subsequently the amount of absorbed dose is pertinent because of its many effects, which include somatic and genetic effects.
Somatic effects are those effects, which do manifest instantly in individual
that encountered the exposure. It can further be classified either as shortterm
recoverable effects or longterm irrecoverable effects. The former involves
effects such as skin infection (deformation) which can be cured or recovered
from within given period of time, while the latter involves infection such as
cataract, anemia, tumor etc., which can not be cured or recovered from, rather
it is terminal (Lagarde, 2003; Motersill et al., 2002; Prokic et
al., 2002; Gransty and LaMarre, 2004).
Genetic effects on the other hand are these effects that do not manifest instantly but in a later generation such as abnormal nails and toes, mutation of the chromosomes, which results in changes in physical features of offspring (UNSCEAR, 1988).
Development of the model: Average Time Spent Indoor or outdoor by urban and rural dwellers per day is expressed in terms of the exposure rate. The rate at which an individual is exposed to radiation (exposure rate) can be expressed as:
where t is the exposure time, N is the absorbed radiation.
This means that the total amount of radiation (solar, ionizing and nonionizing)
absorbed by any individual is directly proportional to the time of exposure.
The steps employed in estimating the time spent outdoor in order to predict
the exposure rate is hereby presented. The following assumptions are considered
appropriate as to properly account for all the activities considered to be outdoor.
• 
The activities can either be classified as indoor or outdoor. 
• 
The activities are considered as variables (independent). 
• 
The percentage of the time slots for indoor or outdoor activities is considered
as parameters. 
• 
Each activity has a component or percentage of indoor and outdoor. 
• 
Everyone living in the urban or rural area, has something doing at any
particular time, in other words, no one is idle. 
• 
The activities are hereby classified as follows: Academics/Occupation,
Sleep/Rest, Leisure and other activities. Other activities include the ones
outside academics/occupation, leisure and sleep/rest, i.e., miscellaneous
activities 
• 
It is also assumed that sleeping time is an indoor activity and it takes
an average of 8 h out of the 24 h a day (Brown, 1983). 
• 
Absorbed radiation increases with time spent outdoors. 
A relationship between the timespent indoor or outdoor, which is the dependent
variable and the various factors/activities, which forms the independent variables,
is to be developed. Table 1 presents the parameters that have
been used in the development. It is obvious that each factor (variable) has
components of indoor and outdoor, which could be calculated in percentage. The
total time spent indoors and outdoors per day is 24 h.
Let the time spent for indoors be X, the time spent outdoors be Y and the total time spent indoor and outdoor be Z. Hence
Since X and Y are considered in this work to depend on four variables as presented in Table 1, X and Y are therefore function of L, A, M and R i.e., X = f (L, A, M, R) and Y = f (L, A, M, R).
It is also assumed that X and Y are linearly related to L, A, M, R, since each independent variable operates separately and tend to follow a regular sequence (Lagarde, 2003; Motersill et al., 2002; Cross and Moscardini, 1985; Edwards and Horton, 1989; Hocking, 1984). However, each independent variable or activity depends on a parameter, which is a fraction or percentage of the time slot for each activity. Hence
Table 1: 
Parameters
adopted in developing the model 

Equation 3 and 4 are continuous and they
depend on the number of variables to be considered. In this study, four variables
were considered. Equation 3 and 4 therefore
become
Making Y the subject in Eq. 2, we obtain
Substituting X of Eq. 3 into Eq. 7, we obtain
Adding 6 and 8, we obtain
Similarly
Declaring a new function, let
By induction therefore, it would be convenient to represent the four parameters of Eq. 12 with a generalized equation given as (4)
Thus Eq. 10 and 11 can be represented
by
Equation 14 and 15 are the mathematical
representation that was employed to determine the time spent indoor and outdoor
by any person living either in an urban or rural environment. In a more concise
manner, they can be written as
where L_{i} represent the variables and T_{i} represents the parameters. The values of these parameters T_{i} can be calculated from the relative percentage spent indoor and outdoor of the timeslot for each activity.
Using the model and data acquisition: In obtaining the appropriate values
of the variables and their corresponding model parameters, questionnaire was
administered to people residing at Lagos State and Benin City representing urban
dwellers and some villages in Edo State representing rural dwellers. In order
to consider a larger proportion of the populace, people were grouped based on
the closeness and similarities of their activities. It was assumed that the
sampled population is engaged in one activity or the other, either schooling
(student) or working (workers). For convenience, we have not considered the
nonworking class, though the models described by Eq. 16
and 17 can be used to accommodate the nonworking class (including
Pensioners, Job seekers and full house wife). The timeslot for occupation of
the aforementioned group of people would be taken as zero. The time spent for
other activities and the percentage indoor and outdoor for each of the activities
will vary from person to person. The summary of the average time slot for urban
dwellers for each of the activity is presented in Table 2
while Table 3 presents the values of T_{i} estimated
from α_{i} and β_{i} for each of the activities. Similar
presentations have been made for rural dwellers in Table 4
and 5.
Equation 16 and 17 have been solved by
developing FORTRAN subroutine to evaluate numerically the time spent for indoor
and outdoor activities using their dependable variables.
Table 2: 
The
summary of the average time slot for urban dwellers for each of the activity
for the eight groups of people considered in this study 

Table 3: 
Values
of T_{i} estimated from α_{i} and β_{i }for
each of the activity as applicable to urban dwellers 

Table 4: 
The
summary of the average time slot for rural dwellers for each of the activity
for the four groups of people considered in this study 

Table 5: 
Values
of T_{i }estimated from α_{i }and β_{i }for
each of the activity as applicable to rural dwellers 

Table 6: 
The
results of the computation of time spent outdoor for urban and rural dwellers 

RESULTS AND DISCUSSION
The results of the computation are presented in Table 6 for urban and rural dwellers. The average time spent for outdoor activity by an average city dweller has been calculated to be 4.88 h. This is the mean average time of the data presented in Table 6. Similarly, the average time spent for outdoor activity by an average rural dweller has been calculated to be 6.45 h. This implies that average city dwellers spent 20.33% of the total time per day exposed to atmospheric radiation while an average rural dweller spent 26.88% of the time per day exposed to atmospheric radiation. This time of exposure is enough to cause a large accumulation of both radioactive and solar radiation and dose in the body, which could result to several side effects. These effects can results to sickness or infections, which could be terminal in nature.
The sample variance for the data presented in Table 6 for urban and rural dwellers are 2.489 and 2.46, respectively. This enables us to estimate the extent of deviation from the mean value in order to predict the confidential interval. It follows therefore that the time spent by average city dweller for outdoor activities is between 2.391 and 7.369 h, while the time spent by an average rural dweller for outdoor activities is between 3.99 and 8.91 h. Rural dwellers are more exposed to atmospheric radiation than city dwellers. This follows therefore that rural dwellers absorb more radiation than urban dwellers. This is likely responsible for the high rate of skin infections (deformation) such as tumor, cataracts, abnormal nail and short life span among rural dwellers.
CONCLUSIONS
We have attempted, in this study, to develop a mathematical representation
of the time spent for outdoor and indoor activities by urban and rural dwellers.
The mathematical model representation has been used to calculate the occupancy
factor for outdoor activities by urban and rural dwellers. The occupancy factor
for city dweller is between 2.391 and 7.369 h with a mean of 4.88 h, while that
rural dweller is between 3.99 and 8.91 h with a mean of 6.45 h. This corresponds
to the time for radiation exposure and absorption during the day time. This
in turn would predict the total amount of radiation absorbed, given the exposure
rate for the urban and rural populace. This is of a particular interest in the
determination of dose from nuclear radiations released into the environment
from nuclear accident, nuclear weapon test and UV radiation.
The model presented in this research for the city and rural dwellers can also be used as an economic index to determine the level of productivity in a given population.