Let $\mathcal{C}(\mathbb{R})$ be the $\mathbb{R}$-vector space of continuous functions from $\mathbb{R}$ to $\mathbb{R}$. Let $a_1, a_2, a_3$ be distinct real numbers. For $i = 1, 2, 3$, let $f_i \in \mathcal{C}(\mathbb{R})$ be the function $f_i(t) = e^{a_i t}$. Which of the following statement(s) is/are true?\\
(A) $f_1, f_2$ and $f_3$ are linearly independent.\\
(B) $f_1, f_2$ and $f_3$ are linearly dependent.\\
(C) $f_1, f_2$ and $f_3$ form a basis of $\mathcal{C}(\mathbb{R})$.