How many solutions of $a+b\sin t= t^n$ on $(0,+\infty)$

Question

When I was in secondary school, I saw a question how many intersection of $\sin t$ and $t^n$ on $(0,+\infty)$, where $n$ is positive interger. It is not hard to answer. But general this question, how many solutions of $$ a+b\sin t= t^n $$ where $a,b\in \mathbb R$ are constant, $n$ is positive interger . Obviously, it should be presented by $a,b,n$. But I really can't desolve it. How to do it ?