#### Answer

See the full explanation below.

#### Work Step by Step

(a)
Consider the provided statement “According to the National Center for Health Statistics, in 1990, 28% of babies in the United States were born to parents who were not married. Throughout the $1990\text{s}$ this percentage increased by approximately 0.6 per year.”
Thus, to express the percentage of babies born out of wedlock, we use P as a function of the number of years after 1990:
$P\left( x \right)=mx+b$.
Suppose that x represents the percentage of babies born after $1954$.
The percentage of babies born out of wedlock in 1990 is 28% and this percentage is increased by $0.6$ per year, that is $28+\left( 0.6 \right)x$.
Thus, by above given conditions
$P\left( x \right)=28+0.6x$
Hence, to express the percentage of babies born out of wedlock after 1990:
$P\left( x \right)=28+0.6x$.
(b)
Consider the provided statement “According to the National Center for Health Statistics, in 1990, 28% of babies in the United States were born to parents who were not married. Throughout the $1990\text{s}$ , this percentage increased by approximately 0.6 per year.”
Thus, to calculate the year in which 40% of babies were born out of wedlock use the linear function representing the percentage of babies born of the form $P\left( x \right)=28+0.6x$ from part (a).
Therefore, from the above given condition.
$\begin{align}
& P\left( x \right)=28+0.6x \\
& 40=28+0.6x \\
& 12=0.3x \\
& 20=x
\end{align}$
Hence, the year in which 40% of babies were born out of wedlock is $\text{20 years}$ after 1990, in 2010.