Answer
(a.) Difference function is $=-0.1x+6$.
(b.) $ 4 $ million.
(c.) best fit.
Work Step by Step
The given two functions are
For male U.S. population $ M(x)=1.5x+115 $.
where, $ M(x) $ is in millions and $ x $ is number of years after $ 1985 $.
For female U.S. population $ F(x)=1.4x+121 $.
Where, $ F(x) $ is in millions and $ x $ is number of years after $ 1985 $.
(a.) The function that models the difference is
$ D(x)=F(x)-M(x) $
$ D(x)=1.4x+121-1.5x-115 $
Add like terms.
$ D(x)=-0.1x+6$.
(b.) The value of $ x $ for U.S. population in $ 2005 $.
$ x=2005-1985 =20 $
Substitute into the difference function of the U.S. population.
$ D(20)=-0.1(20)+6 $.
$ D(20)=-2+6 $
$ D(20)=4 $
(c.) Actual difference between the female and male population in $ 2005 $ is
$ = 151-147 $
$ =4 $
The result in part (b) is best fit for the actual value.
