Answer
Not one-to-one.
Work Step by Step
You can stagnate in your height (pause growing) for some time, or even shrink (old people start shrinking). In both cases, the same height can correspond to different age $t$. (You can be $1.75$ m tall when you are $16$, then grow to $1.8$ m when you are $21$ and shrink back to $1.75$ when you are $65$).
