Answer
No, the percent of deaths due to smoking approach to $100\%$ , but never attain it.
Work Step by Step
As the degree of the numerator and denominator are equal, the ratio in the numerator and denominator of the coefficient of x in $P\left( x \right)$ gives the horizontal asymptote.
The coefficients of x in the numerator and denominator of $P\left( x \right)$ are 100 and 1 respectively.
The horizontal asymptote of the graph of $P\left( x \right)$ is
$\frac{100}{1}=100$
This mean the graph of $P\left( x \right)$ approaches $100\%$.
The percent of deaths due to smoking approach to $100\%$ , but never get to $100\%$ exactly.
