We need the growth constant for both A and B, but it is only given for A.

 Culture B doubles every 3.00 days, therefore:

ln 2 = 3 kB
kB = 0.231 day-1

 Now we have for any time t:
NA = 1000e0.05t and NB = 1500e0.231t

 The question asks: How long until culture B has p times as many cells as culture A?
This means:

(a) NB = pNA
(b) NA = pNB
(c) NB = NA + p