#### Answer

a. $P(x)= 2.92x+236$ (millions)
b. $R(x)=\frac{1.48x + 115.1}{2.92x+272}$
c. $y\approx0.51$

#### Work Step by Step

a. The total population is the sum of the two functions:
$P(x)=M(x)+F(x)=1.48x + 115.1+1.44x + 120.9=2.92x+236$ (millions)
b. The function of men in the total population is given by
$R(x)=\frac{1.48x + 115.1}{2.92x+272}$
c. To obtain the horizontal asymptote of the above function, let $x\to\infty$
We have
$y=\lim_{x\to\infty}\frac{1.48 + 115.1/x}{2.92+272/x}=\frac{1.48}{2.92}\approx0.51$
This means that the percentage of men in the US population will approach 0.51 over time.