experiment/ word problem help

Quote:

2.6 A seed crystal of diameter D (mm) is placed in a solution of dissolved salt, and

new crystals are observed to nucleate (form) at a constant rate $\displaystyle r (crystals \\\\ min^{-1}) $ .

Experiments with seed crystals of differentt sizes show that the rate of nucleation

varies with the seed crystal diameter as

$\displaystyle r(crystals\\ min^{-1}) = AD + BD^{2} $

where D is in mm, and where A and B are constants (which must be determined).

(a) What are the units of the constants A and B? Suppose that a D = 1 mm

seed crystal produces a nucleation rate of r = 210 crystals min��1, whereas a

D = 2 mm seed crystal produces a nucleation rate of r = 440 crystals min��1.

Use this information to evaluate A and B.

(b) Calculate the crystal nucleation rate in crystals min��1 for a seed crystal di-

ameter of 0.05 inch.

(c) Derive a formula for r (crystals min��1) in terms of D (in). What are the

values and units of the constants in the expression? Check the formula with

the result of 2.6(b). Comment on your results.

(d) Derive a formula for $\displaystyle r (crystals s^{-1}) $ . what are the values snd units of the constants in the expression.

for part 'a', I got the units of A and B, as $\displaystyle crystals\\\\\\ min^{-1} mm^{-1} $ for A

$\displaystyle crystals\\\\\\\\ min^{-1} mm^{-2} $ for B

so the mm would cancels out, with the D units, and the equation balances. is this correct?

Also worked out A = 200 and B =10

so equation would look something like this,

$\displaystyle r( crystals \\\\\ min^{-1} ) = \frac{200 Dmm\\\\\ crystals}{min\\\\ mm} + \frac{10Dmm^{2} \\\\\\crystals}{min\\\ mm^{2}} $

b) = $\displaystyle r = 200(1.27) + 10(1.27)^{2} $

c) ? Really Need help with part c. Do I just replace the units for diameter in my equation?