Answer
a. $\frac{1.75x^2-15.9x+160}{2.1x^2-3.5x+296}$
b. $67\%$
c. $66\%$; underestimates by $1\%$
d. $y=\frac{5}{6}$, $83\ (\%)$
Work Step by Step
a. Using the given equations, we have
$r(x)=\frac{p(x)}{q(x)}=\frac{1.75x^2-15.9x+160}{2.1x^2-3.5x+296}$
b. Using the given graph, in 2010, the ratio is
$\frac{25040}{37207}\approx67\ (\%)$
c. For year 2010, $x=2010-1970=40$
Wwe have
$r(40)=\frac{1.75(40)^2-15.9(40)+160}{2.1(40)^2-3.5(40)+296}\approx66\ (\%)$ .
This underestimates the value by $1\%$ compared with the value from part-b.
d. When $x\to\infty$, we have
$r\to\frac{1.75}{2.1}=\frac{5}{6}$
Thus the asymptote is $y=\frac{5}{6}$. For a long time, the percentage will be $\frac{5}{6}\approx83\ (\%)$
