60 minutes is exactly 6 half-lives, so the decay for 60 minutes will produce 1/2^6, or 1/64 of the initial activity.
But the amount was not given in activity units, it was given in mass units.
Also, since nitrogen does not exist as single atoms and the compound was not given, you need to assume that the mass refers to only nitrogen, as if it were pure N-13 N2 gas (which is physically impossible to have).
The problem is also unrealistic in that you would never be presented with the weighed mass of something like N-13, you'd have to calculate it from the radioactivity.
However... 1.49 ug/MW of N-13 (MW =13 of course) is 0.115 umoles. Converting by Avogadro's number, this is 6.9E16 atoms.
The radioactivity produced by N atoms is lambda*N where lambda is the decay constant, which is equal to ln(2)/half-life.
So lambda is 0.00115 sec-1 and the decay rate is this times 6.9E16 atoms, or 7.97E13 decays per second.
A Ci is 3.7E10 dps, so the starting activity is a whopping 2100 Ci. (a highly unrealistic number) Divide this by the decay factor to get 33 Ci after an hour.