Answer
Makes sense
Work Step by Step
The rules for finding the horizontal asymptote of rational function is as follows:
1. If the numerator's degree is less than the denominator's degree, there is a horizontal asymptote at $y = 0$.
2. If the numerator's degree equals the denominator's degree, there is a horizontal asymptote at $y = c$, where $c$ is the ratio of the leading terms or their coefficients.
3. If the numerator's degree is more than the denominator's degree, then there is no horizontal asymptote.
$f(x)=\frac{1.96x+3.14}{3.04x+21.79}$
In this case, the degree of the numerator is equal to the degree of the denominator. Therefore, the horizontal asymptote is as follows
$y=\frac{1.96}{3.04}=\frac{1.96}{3.04}\times 100=0.6447\times 100=64.47\%$.
meaning, the percentage of the prisoner approaches $64.47\%$ as time goes on or may even cross it.
As $64.47>60$ the statement makes sense.
