Answer
(a) $y = 3,000$
(b) As time passes, and the number of bass in the lake increases, eventually they reach a limit of $3,000$ in the lake.
Work Step by Step
To find the horizontal asymptote of this rational function, we must first identify the degree of the functions in both the numerator and the denominator: $$f(x) = \frac{150x + 120}{0.05x + 1}$$ Since both are linear functions, their degrees are the same: $1$. In this case, the horizontal asymptote is determined as the ratio of the leading coefficients, that is to say: $$y_{asymptote} = \frac{150}{0.05} = 3,000$$ What can we interpret from this? That as $x → ∞$, $f(x)$ approaches $3,000$. For the purposes of this exercise, this means that, no matter how much time $x_{months}$ passes, the maximum number of bass will level off at 3,000.
