Delay in the transmission of knowledge to poorer countries
By the notation used, labor quantity appears to be constant. Then the only source of growth of output is the growth in $A_N(t)$, and they will have the same growth rate. Take logarithms and then time derivatives on the output per capita equation to see this.
Then remember introductory differential equations on how to express $x(t)$ as a function of $x(0)$ and a constant growth rate. And don't forget to explicitly solve for the 10-factor difference required, at the end.