. Biophysics: concepts and mechanisms. Biophysics. 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 = mx2 -f b is a parabolic rational function. In the case of the area of a spherical cell, the value, A, increases faster than that
. Biophysics: concepts and mechanisms. Biophysics. 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 = mx2 -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/N0 = e~kl is an exponential rational function, in this case a decay (minus sign) or lessening, as time / increases, of the fraction N/N0i where JV0 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 Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original Casey, Edmund Jeremiah, 1924-. New York, Reinhold Pub. Corp
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