Pharmacology for Anaesthesia and Intensive Care

P1: PCX Printer: Yet To Come
9780521704632c06 CUFX213A/Peck 9780521618168 December 27, 2007 14:11

Section IBasic principles

A

B

x

y

B

A

y

x

asymptote

S

(a)

(b)

Figure 6.4.Comparison of rectangular hyperbola and exponential curves.(a) Curve A is

anegative exponential (y=Ae−ax), curve B is a positive rectangular hyperbola (y=1/x).

(b) Curve A is still a negative exponential (y=S(1−e−ax)) but curve B is now a negative

rectangular hyperbola (y=S−1/x). Both graphs have effectively been reflected in the

x-axis and moved upward in relation to the y-axis.

Furthermore, we can convert any expression such as z=w10yto its logarithmic

equivalent. In this case:

log(z)=log(w10y).

Because w10y=w× 10 yand we add the logarithms of numbers that are multiplied

together this can be written:

log(z)=log(w)+log(10y).

Tofind log(10y)weneed to remember that logarithms represent the power to which

10 is raised to give the required number. Thus, 1000= 103 = 10 × 10 ×10 and