Answer:
The horizontal asymptote represents the terminal population of the trout.
Step-by-step explanation:
The horizontal asymptote of the given rational function is the limit of [tex]p(t)[/tex] when [tex]t \to +\infty[/tex]. That is:
[tex]\lim_{t \to \infty} p(t) = \lim_{t \to \infty} \frac{150\cdot t + 100}{0.04\cdot t + 1}[/tex] (1)
Then, we apply the concept of limits for rational-polynomial functions:
[tex]\lim_{t \to \infty} \frac{\frac{150\cdot t}{t} + \frac{100}{t}}{\frac{0.04\cdot t}{t} + \frac{1}{t} }[/tex]
[tex]\lim_{t \to \infty} p(t) = 3750[/tex]
The horizontal asymptote represents the terminal population of the trout. In this case, the terminal population of the trout is 3750.
