Chapter 7, Problem 21PTTS

a.

To determine

To make: A data display showing the population for those years.

Answer to Problem 21PTTS

The population of those years has been shown in the $\text{table}\text{.1}$

Explanation of Solution

Given information: The table shows the population of Washington D.C., every $10$ years from $1950\text{ to 2000}$ .

Year	$1950$	$1960$	$1970$	$1980$	$1990$	$2000$
Population	$802,000$	$764,000$	$757,000$	$638,000$	$607,000$	$572,000$

Calculation:

Population change from $1950\text{ to 1960 is (802,000}-764,000)=38,000$

Decreasing rate of population for these $10$ years is;

  $\begin{array}{l}=\frac{38,000}{10}\\ =3800\end{array}$

Similarly, Population change from $1960\text{ to 1970 is (764,000}-757,000)=7000$

Decreasing rate of population for these $10$ years is;

  $\begin{array}{l}=\frac{7000}{10}\\ =700\end{array}$

Similarly, Population change from $1970\text{ to 1980 is (757,000}-638,000)=119000$

Decreasing rate of population for these $10$ years is;

  $\begin{array}{l}=\frac{119,000}{10}\\ =11900\end{array}$

Similarly, Population change from $1980\text{ to 1990 is (638,000}-607,000)=31,000$

Decreasing rate of population for these $10$ years is;

  $\begin{array}{l}=\frac{31,000}{10}\\ =3100\end{array}$

Similarly, Population change from $1990\text{ to 2000 is (607,000}-572,000)=35,000$

Decreasing rate of population for these $10$ years is;

  $\begin{array}{l}=\frac{35,000}{10}\\ =3500\end{array}$

Let’s display the data of population of those years,

  $\text{Table}\text{.1}$

Year	Population
$1950$	$802,000$
$1951$	$\begin{array}{l}802,000-3800\\ =798,200\end{array}$
$1952$	$\begin{array}{l}\text{ 798},200-3800\\ =794,400\end{array}$
$1953$	$\begin{array}{l}\text{ 794},400-3800\\ =790,600\end{array}$
$1954$	$\begin{array}{l}\text{ 790},600-3800\\ =786,800\end{array}$
$1955$	$\begin{array}{l}\text{ 786},800-3800\\ =783,000\end{array}$
$1956$	$\begin{array}{l}\text{ 783},000-3800\\ =779,200\end{array}$
$1957$	$\begin{array}{l}\text{ 779},200-3800\\ =775,400\end{array}$
$1958$	$\begin{array}{l}\text{ 775},400-3800\\ =771,600\end{array}$
$1959$	$\begin{array}{l}\text{ 771},600-3800\\ =767,800\end{array}$
$1960$	$764,000$
$1961$	$\begin{array}{l}\text{ 764},000-700\\ =763,300\end{array}$
$1962$	$\begin{array}{l}\text{ 763},300-700\\ =762,600\end{array}$
$1963$	$\begin{array}{l}\text{ 762},600-700\\ =761,900\end{array}$
$1964$	$\begin{array}{l}\text{ 761},900-700\\ =761,200\end{array}$
$1965$	$\begin{array}{l}\text{ 761},200-700\\ =760,500\end{array}$
$1966$	$\begin{array}{l}\text{ 760},500-700\\ =759,800\end{array}$
$1967$	$\begin{array}{l}\text{ 759},800-700\\ =759,100\end{array}$
$1968$	$\begin{array}{l}\text{ 759},100-700\\ =758,400\end{array}$
$1969$	$\begin{array}{l}\text{ 758},400-700\\ =757,700\end{array}$
$1970$	$757,000$
$1971$	$\begin{array}{l}\text{ 757},000-119,00\\ =745,100\end{array}$
$1972$	$\begin{array}{l}\text{ 745},100-119,00\\ =733,200\end{array}$
$1973$	$\begin{array}{l}\text{ 733},200-119,00\\ =721,300\end{array}$
$1974$	$\begin{array}{l}\text{ 721},300-119,00\\ =709,400\end{array}$
$1975$	$\begin{array}{l}\text{ 709},400-119,00\\ =697,500\end{array}$
$1976$	$\begin{array}{l}\text{ 697},500-119,00\\ =685,600\end{array}$
$1977$	$\begin{array}{l}\text{ 685},600-119,00\\ =673,700\end{array}$
$1978$	$\begin{array}{l}\text{ 673},700-119,00\\ =661,800\end{array}$
$1979$	$\begin{array}{l}\text{ 661},800-119,00\\ =649,900\end{array}$
$1980$	$638,000$
$1981$	$\begin{array}{l}\text{ 638},000-3100\\ =634,900\end{array}$
$1982$	$\begin{array}{l}\text{ 634},900-3100\\ =631,800\end{array}$
$1983$	$\begin{array}{l}\text{ 631},800-3100\\ =628,700\end{array}$
$1984$	$\begin{array}{l}\text{ 628},700-3100\\ =625,600\end{array}$
$1985$	$\begin{array}{l}\text{ 625},600-3100\\ =622,500\end{array}$
$1986$	$\begin{array}{l}\text{ 622},500-3100\\ =619,400\end{array}$
$1987$	$\begin{array}{l}\text{ 619},400-3100\\ =616,300\end{array}$
$1988$	$\begin{array}{l}\text{ 616},300-3100\\ =613,200\end{array}$
$1989$	$\begin{array}{l}\text{ 613},200-3100\\ =610,100\end{array}$
$1990$	$607,000$
$1991$	$\begin{array}{l}\text{ 607},000-3500\\ =603,500\end{array}$
$1992$	$\begin{array}{l}\text{ 603},500-3500\\ =600,000\end{array}$
$1993$	$\begin{array}{l}\text{ 600},000-3500\\ =596,500\end{array}$
$1994$	$\begin{array}{l}\text{ 596},500-3500\\ =593,000\end{array}$
$1995$	$\begin{array}{l}\text{ 593,000}-3500\\ =589,500\end{array}$
$1996$	$\begin{array}{l}\text{ 589,500}-3500\\ =586,000\end{array}$
$1997$	$\begin{array}{l}\text{ 586,000}-3500\\ =582,500\end{array}$
$1998$	$\begin{array}{l}\text{ 582,500}-3500\\ =579,000\end{array}$
$2000$	$572,000$

Hence, The population of those years has been shown in the $\text{table}\text{.1}$ .

b.

To determine

To find: The year in which the population decrease the most from $10\text{ years}$ earlier, and the approximate percentage of change.

Answer to Problem 21PTTS

In the year $1970$ the population decrease the most from $10\text{ years}$ earlier and The approximate percent of change is $15.72\%$ .

Explanation of Solution

Given information: The table shows the population of Washington D.C., every $10$ years from $1950\text{ to 2000}$ .

Year	$1950$	$1960$	$1970$	$1980$	$1990$	$2000$
Population	$802,000$	$764,000$	$757,000$	$638,000$	$607,000$	$572,000$

Calculation:

The decrease rate in $1950\text{ to 1960}$ is $3800$ .

The decrease rate in $1980\text{ to 1970}$ is $700$

The decrease rate in $1970\text{ to 1980}$ is $119,00$

The decrease rate in $1980\text{ to 1990}$ is $3100$

The decrease rate in $1990\text{ to 2000}$ is $3500$

Hence, It is observed from the data table of population that $1970$ is the year in which the population decrease the most from $10\text{ years}$ earlier.

Let’s find the percent of change;

  $\begin{array}{l}=\frac{11900}{757,000}\times 100\\ =\frac{11900}{757}\\ =15.72\%\end{array}$

Hence,

In the year $1970$ the population decrease the most from $10\text{ years}$ earlier and The approximate percent of change is $15.72\%$ .

c.

To determine

To conclude: The population of Washington D.C. has decrease every year from $1950$ .

Answer to Problem 21PTTS

Yes, the population of Washington D.C. has decrease every year from $1950$ .

Explanation of Solution

Given information: The table shows the population of Washington D.C., every $10$ years from $1950\text{ to 2000}$ .

Year	$1950$	$1960$	$1970$	$1980$	$1990$	$2000$
Population	$802,000$	$764,000$	$757,000$	$638,000$	$607,000$	$572,000$

Calculation:

From, The dada table of population it is clear that the population from the year $1950\text{ to 2000}$ is in a decreasing order.

Conclusion:

Hence, It can be concluded that the population of Washington D.C. has decrease every year from $1950$ .