Answer
(a.) The function is $=\frac{1.5x+115}{1.4x+121} $.
(b.) The ratio is $ 0.968 $.
(c.) Overestimate the actual value by $\$ 0.003 $ million.
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 Ratio is
$ R(x)=\frac{M(x)}{F(x)} $
Substitute values.
$ R(x)=\frac{1.5x+115}{1.4x+121} $.
(b.) The value of $ x $ for U.S. population in $ 2000 $.
$ x=2000-1985 =15 $
Substitute into the ratio function U.S. population.
$ R(x)=\frac{1.5(15)+115}{1.4(15)+121} $
$ R(x)=\frac{22.5+115}{21+121} $
$ R(x)=\frac{137.5}{142} $
$ R(x)=0.96830985915 $
Correct to three decimal places
$ R(x)=0.968 $.
(c.) Actual ratio of male to female population in $ 2000 $ is
$ = \frac{138}{143} $
$ =0.965 $
The result in part (b) is overestimate the actual value by.
$ 0.968-0.965 = 0.003 $.
