Answer:
n = 9
Explanation:
To find the answer we need to check at what point the running time of algorithm A is equal the running time of B:
1000*n*n = n*n*n*n*n Â
1000 = n*n*n = n^3
n = ∛(1000) = 10  (when n equals ten A equal B)
For any integer greater than ten B > A Â and for any integer smaller than ten B < A. The greatest integer for which B < A is nine, therefore nine is our answer. Â
          A                    B
          1000n^2              n^5
n = 8 Â Â Â Â Â Â 64000 Â Â Â Â Â Â Â < Â Â Â Â Â Â 32768
n = 9 Â Â Â Â Â Â 81000 Â Â Â Â Â Â Â < Â Â Â Â Â Â 59049
n = 10 Â Â Â Â Â Â 100000 Â Â Â Â Â Â = Â Â Â Â Â Â 100000
n = 11 Â Â Â Â Â Â 121000 Â Â Â Â Â Â > Â Â Â Â Â Â 161051
n = 12 Â Â Â Â Â Â 144000 Â Â Â Â Â Â > Â Â Â Â Â Â 248832
