Decay in the size of object as we move away Size of Object = # of pixels falling on the object
The object is of arbitrary dimensions, so if we take photos of object from 1 meter distance, then 2 meter distance and so on. The number of pixels falling on the object will decrease. I want to know how will they decrease linearly or exponentially.
 A: If $r$ is the distance then $4 \pi r^2$ is the area of a sphere at that distance surrounding us
The object has area $A$
The fraction of the sphere it takes up is $f=\dfrac{A}{4\pi r^2}$
Thus the number of pixels it falls upon will be proportional to $r^{-2}$
A: Zephyr's answer is good but does not comment on your use of exponential.  You say "linearly or exponentially" as if it must be one or the other.  This is not so and, in fact, in this case it is neither.
Outside of science and mathematics, it is common to say exponential just to mean grows fast.  Even among computer programmers, I have often heard exponential used to mean faster than linear but, more precisely, it refers to a specific growth pattern in which one quantity increases or decreases by a constant factor in relation to another which changes in equal steps.  So, $1, 2, 4, 8, 16, ...$ is an example of exponential growth, each factor is $2 \times$ the previous one. Similarly, $1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, ...$ is an example of exponential decay.  There are many ways that something may grow faster than linear but slower than exponential.  A common one is quadratic e.g. $1, 4, 9, 16, 25, ...$.
Exponential growth is generally regarded as very fast but the factor could be very small and it might not seem so at first.  It is fast in a sense which is that something growing exponentially will eventually overtake something growing quadratically, cubically, or by another power.  It is not the fastest, there is no fastest.  A simple example of one that is faster is factorial.
