The cross-sectional diameter of a laser as it is focused through a lens is given by d(z) =

p az2 + bz + c, where d(z) is the beam diameter (with units of mm), z is the distance (in mm) the measurement is taken relative to the focusing lens, and

a, b, c are constant for any particular laser

(although different lasers will have different values). Typical experimental data are shown in Fig. 3.11.

a. What are the units of

a, b and c?

b. Let a = 0.006, b = −1.14, and c = 55.4

(in whatever units you calculated in part (a)). What is the mathematical domain and range of this function? What is the scientific domain and range? 4.9 If ln(x) = 4 what is log10(x)?

If log10(x) = 4 what is ln(x)?