Every night, Verizon has to update its database of every customers telephone number. To enable fast lookups, the database includes an index that is a sorted list of all its phone numbers. This index must be rebuilt each night by re-sorting the contents of the database. Verizon has hired you as a consultant to analyze their computing needs for the nightly sorting run. After carefully checking GitHub, you have found three sorting algorithms A, B, and C that can sort n phone numbers in 2 10^-7n², 10⁵n log₂n, and 1.5 10⁴n seconds respectively on a single processor.

What is the smallest problem size n₀ such that algorithm B is strictly faster than algorithm A for all n n₀? (Hint: I dont know of an analytical solution to this problem, so try plugging in values for nor use Newtons method.) Justify your approach.