Chapter 2.5, Problem 38E

(a)

To determine

To graph: A scatter plot of the data

$\begin{array}{l}\begin{array}{ccccccc}\text{Year}& \text{1950}& \text{1960}& \text{1970}& \text{1980}& \text{1990}& \text{2000}\\ \begin{array}{l}\text{Population}\\ \text{(millions)}\end{array}& \text{160}\text{.1}& 190.2& 214.8& 235.1& 259.6& 287.9\end{array}\\ \begin{array}{ccccccc}\text{Year}& \text{2010}& \text{2015}& \text{2020}& \text{2030}& \text{2040}& \text{2050}\\ \begin{array}{l}\text{Population}\\ \text{(millions)}\end{array}& \text{315}\text{.2}& 328.4& 342.9& 369.5& 390.8& 409.1\end{array}\end{array}$

with $x$ as number of years past $1950$ and $y$ as U.S. population in millions.

(b)

To determine

At least two function types that could be used for the data

$\begin{array}{l}\begin{array}{ccccccc}\text{Year}& \text{1950}& \text{1960}& \text{1970}& \text{1980}& \text{1990}& \text{2000}\\ \begin{array}{l}\text{Population}\\ \text{(millions)}\end{array}& \text{160}\text{.1}& 190.2& 214.8& 235.1& 259.6& 287.9\end{array}\\ \begin{array}{ccccccc}\text{Year}& \text{2010}& \text{2015}& \text{2020}& \text{2030}& \text{2040}& \text{2050}\\ \begin{array}{l}\text{Population}\\ \text{(millions)}\end{array}& \text{315}\text{.2}& 328.4& 342.9& 369.5& 390.8& 409.1\end{array}\end{array}$

using scatter plot from part (a).

(c)

To determine

The model, linear or quadratic, that accurately approximates the data points for the year $2040$.

(d)

To determine

The year when the U.S. population is predicted to reach $425$ million, using linear model.