1. The problem is to understand the definition of a function $f(t)$ being of exponential order $e^{\alpha t}$.\n\n2. A function $f(t)$ is said to be of exponential order $e^{\alpha t}$ if there exist real constants $M > 0$ and $N > 0$ such that for all $t > N$, the inequality $|f(t)| < M e^{\alpha t}$ holds.\n\n3. This means that beyond some time $N$, the function $f(t)$ does not grow faster than the exponential function $M e^{\alpha t}$.\n\n4. The constants $M$ and $N$ serve as bounds to control the growth of $f(t)$, ensuring it is dominated by an exponential function with rate $\alpha$.\n\n5. This concept is important in analysis and differential equations to classify functions based on their growth rates and to apply certain transforms like the Laplace transform.