Algebra 2 · Hard problem

City $A$'s population is modeled by $P_A(t) = 50{,}000(1.02)^t$ and city $B$'s by $P_B(t) = 40{,}000(1.035)^t$, with $t$ in years. After how many full years will city $B$'s population first exceed city $A$'s?