10 THE SYSTEMS CONCEPT 



(b) parabolic, and (c) exponential. The periodic functions are transcenden- 

 tal (see Figure 1-2). 



Figure 1-2. The Graphical Shape of Some Important Functional Relationships Defined 



in the Text. 



(a) y = kx is a linear rational function and j> plotted against x is a straight 

 line of the form y = mx + b, with b = 0. The ideal gas law, PV = 

 nRT, again can be used as a pertinent example. 



(b) y = mx 2 -f b is a parabolic rational function. In the case of the 

 area of a spherical cell, the value, A, increases faster than that 

 of the radius, r, so that the plot of A( =y) vs r( =x) sweeps up 

 rapidly in a curve toward higher values of A, as r is increased. 



(c) N/N = e~ kl is an exponential rational function, in this case a decay 

 (minus sign) or lessening, as time / increases, of the fraction N/N 0i 

 where JV is the value of JV when t = 0; and A; is a proportionality con- 

 stant. This function has less curvature than the parabolic. Radioac- 

 tive decay is an example. The constant, k, can itself be negative. The 

 weight of a growing baby is an example. 



(c') y = log x is a cousin of (c), called the logarithmic function. It has the 

 same curvature as (c) but a different node. An example is the voltage 

 across the living cell's wall, a voltage which is dependent upon ratio 

 of salt concentrations inside and outside the cell. 



(d) y = k sin / is aperiodic function. The familiar sine wave of alternating 

 current, the volume of the lungs as a function of time, and the pres- 

 sure in the auricle of the heart as a function of time, are all examples. 



Figure 1-2 illustrates the four functional relationships. 



