Let y=ax^b be the function where a and b are constants.
Plug in (3,5103): 5103=a3^b and plug in (2,448): 448=a2^b.
Divide these two equations: 5103/448=(3/2)^b. Take logs: blog(1.5)=log(5103/448).
5103/448=729/64=3^6/2*6=(3/2)^6
So b=6log(3/2)/log(3/2)=6.
Substitute b=6 in y=ax^b=ax^6; so 448=64a and a=448/64=7.
Therefore the function f(x)=7x^6.