Every night, AT&T has to update its database of every customer's 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. AT&T 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 4 10-6n2, 10-4n log2 n, and 1.4 x 10-n seconds respectively on a single processor. 11. What is the smallest problem size no such that algorithm B is strictly faster than algorithm A for all nno? (Hint: Plugging in values for n or using Newton's method are acceptable ways to solve the problem, and you are welcome to use online tools such as Wolfram Alpha and Desmos.) Explain your reasoning. 12. What is the smallest problem size n for which algorithm C is strictly faster than algorithm B for all n ni? Explain your reasoning.