Chapter 4.8, Problem 7CFU

(a)

To determine

To write: A model that relates the percent as a function of the number since 1950.

Answer to Problem 7CFU

  $f\left(x\right)=0.49x+57.7$

Explanation of Solution

Given information: Population: The percent of the United States population living in areas has increased since 1950.

  

Calculation:

Use linear regression

  

  

  

Example:

  $f\left(x\right)=0.49x+57.7$

(b)

To determine

To predict: The percent of the population that will metropolitan area in 2010, using the model.

Answer to Problem 7CFU

  $87.1\text{ percent}$

Explanation of Solution

Given information: Population: The percent of the United States population living in areas has increased since 1950.

  

Calculation:

In 2010, it would be 60 years later, x = 60.

  $\begin{array}{l}f\left(60\right)=0.49\left(60\right)+57.7=87.1\\ 87.1\text{ percent}\end{array}$

(c)

To determine

To predict: What year will have 89% of the population in metropolitan areas, using the model?

Answer to Problem 7CFU

  $2014$

Explanation of Solution

Given information: Population: The percent of the United States population living in areas has increased since 1950.

  

Calculation:

Given the percent answer just set the equation = 89

  $\begin{array}{l}0.49x+57.7=89\\ x=63.88\\ 1950+64=2014\end{array}$