For each function f(n) and time t in the following table, determine the largest size n of a problem that can be solved in time t, assuming that the algorithm to solve the problem takes f(n) microseconds.

We will provide a sample solution on how to solve for a 1sec for each of the running time.
1sec = 1000millisecond = 1000000microsecond
1sec = 10^6microsecond
Solving for
lgn = 10^6
solving for
Solving for
With an initial guess of 10^6, we can use Newton-Raphson method to get a solution
Solution is:

**See https://replit.com/@AleemIsiaka/nlgn-106#main.py Solving for n^3 = 10^6 Solving for Solving for n! n! = n! = 1*2*3*4….n = We could pick a number as a guess, and check if the value is within . if n = 10 10! = 3628800 (> ) 9! = 637120 (< ) Hence n = 9, such that We could do same for the rest of the time, changing the time value but running similar operations for the running times.***62746.12646969076*ㅤ | 1sec | 2minute | 1hr | 1day | 1month | 1year | 1century |

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