Chapter 4.8, Problem 19E

(a)

To determine

To write: A model that relates the median age as a function of the number of years since 1900.

Answer to Problem 19E

  $f\left(x\right)=0.126x+22.732$

Explanation of Solution

Given information: Marketing: The United States Census Bureau has projected the median age of the U.S population to the year 2080. A fast-food chain wants to target its marketing towards customers that are about the median age.

  

Calculation:

Plug the data to get:

  

  

  $f\left(x\right)=0.126x+22.732$

(b)

To determine

To predict:age that the fast-food chain should target in the year 2010, using the model.

Answer to Problem 19E

  $37\text{ years}$

Explanation of Solution

Given information: Marketing: The United States Census Bureau has projected the median age of the U.S population to the year 2080. A fast-food chain wants to target its marketing towards customers that are about the median age.

  

Calculation:

2010 is 110 years from 1900.

  $x=110$

  $f\left(110\right)=0.126\left(110\right)+22.732=36.592\simeq 37$

37 years

(c)

To determine

To predict:age that the fast-food chain should target in the year 2025, using the model.

Answer to Problem 19E

  $38\text{ years}$

Explanation of Solution

Given information: Marketing: The United States Census Bureau has projected the median age of the U.S population to the year 2080. A fast-food chain wants to target its marketing towards customers that are about the median age.

  

Calculation:

2025 is 125 years from 1900.

  $x=125$

  $f\left(125\right)=0.126\left(125\right)+22.732=38.482\simeq 38$

38 years