Is $S = \{\alpha \in \mathbf{R}^3 \mid \alpha_1 + \alpha_2e^{-t} + \alpha_3 e^{-2t} \leq 1.1 \mbox{ for } t\geq 1\}$ affine

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$$S = \{ \alpha \in \mathbf{R}^3 \mid \alpha_1 + \alpha_2e^{-t} + \alpha_3 e^{-2t} \leq 1.1 \mbox{ for } t\geq 1\}$$

Is $S$ affine, and is it a polyhedron?

I thought it's basically a linear function in $\alpha$, thus affine. Since the linear function is characterized by $t$, as $t$ changes, there are many linear functions, thus a polyhedron? Is my reasoning correct, please?

Supplement:

Plotted @A.Γ's equation

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