Answer
a) $D(x)=-0.07x+5.9$
b) $D(20)=4.5$
c) overestimate by $0.5$ million
Work Step by Step
$M(x)=1.53x+114.8$
$F(x)=1.46x+120.7$
a) The function that models the difference between the female population and the male population is: $$D(x)=F(x)-M(x)=(1.53x+114.8)-(1.46x+120.7)=-0.07x+5.9.$$
b) $2005$ is the $2005-1985=20$th year after the year $1985$, therefore, for $2005$, $x=20$. The difference between the female population and the male population in $2005$ is: $$D(20)=-0.07(20)+5.9=4.5.$$
c) This indicates that there were $4.5$ million more female population than male population in the U.S. The difference from the bar graph is $$151-147=4.$$ Because $4.5>4$, the result in part $(b)$ overestimates the actual population difference shown in the bar graph by $4.5-4=0.5$ million.
