## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 1 - Section 1.10 - Modeling with Functions - Exercise Set - Page 291: 4

#### 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.

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