Chapter 6.4, Problem 31IP

a.

To determine

To find: Amount of change and percent change.

Answer to Problem 31IP

City	Population 2000	Population 2006	Amount of change	% of change
Raleigh, NC	$276,093$	$356,321$	$80,228$	$29.1$
Columbia, SC	$116,278$	$119,961$	$3,683$	$3.2$
Frankfort, KY	$27,741$	$27,077$	$-664$	$-2.4$
Columbus, OH	$711,470$	$733,203$	$21,733$	$3.1$

Explanation of Solution

Given information:

Given table shows the population of capital cities for four different states.

Percent of change $=\frac{A}{O}\times 100$

Where

  $A=$ Amount of change.

  $O=$ Original amount.

From given information

For city Raleigh, NC

Amount of change = Final amount $-$ Original amount

  $\begin{array}{l}\Rightarrow A=356,321-276,093\\ \Rightarrow A=80,228\end{array}$

Therefore,

Percent of change $=\frac{80,228}{276,093}\times 100$

  $\Rightarrow$ Percent of change $=\frac{80,22800}{276,093}$

  $\Rightarrow$ Percent of change $=29.058$

To the nearest tenth, the Percent of change is $29.1\%$ .

For city Columbia, SC

Amount of change = Final amount $-$ Original amount

  $\begin{array}{l}\Rightarrow A=119,961-116,278\\ \Rightarrow A=3,683\end{array}$

Therefore,

Percent of change $=\frac{3,683}{116,278}\times 100$

  $\Rightarrow$ Percent of change $=\frac{368,300}{116,278}$

  $\Rightarrow$ Percent of change $=3.1674$

To the nearest tenth, the Percent of change is $3.2\%$ .

For city Frankfort, KY

Amount of change = Final amount $-$ Original amount

  $\begin{array}{l}\Rightarrow A=27,077-27,741\\ \Rightarrow A=-664\end{array}$

Therefore,

Percent of change $=\frac{-664}{27,741}\times 100$

  $\Rightarrow$ Percent of change $=\frac{-66400}{27,741}$

  $\Rightarrow$ Percent of change $=-2.393$

To the nearest tenth, the Percent of change is $2.4\%$ and negative sign indicates that percent is decrease.

For city Columbus, OH

Amount of change = Final amount $-$ Original amount

  $\begin{array}{l}\Rightarrow A=733,203-711,470\\ \Rightarrow A=21,733\end{array}$

Therefore,

Percent of change $=\frac{21,733}{711,470}\times 100$

  $\Rightarrow$ Percent of change $=\frac{21,73300}{711,470}$

  $\Rightarrow$ Percent of change $=3.0546$

To the nearest tenth, the Percent of change is $3.1\%$ .

b.

To determine

To find: Differences and Similarities between Columbia and Columbus.

Answer to Problem 31IP

Percent of change of Columbus and Columbia is almost same.

Amount of change is different for Columbus and Columbia.

Explanation of Solution

Given information:

Given table shows the population of capital cities for four different states.

Concept:

Percent of change $=\frac{A}{O}\times 100$

Where

  $A=$ Amount of change.

  $O=$ Original amount.

For city Columbia, SC

Amount of change = Final amount $-$ Original amount

  $\begin{array}{l}\Rightarrow A=119,961-116,278\\ \Rightarrow A=3,683\end{array}$

Therefore,

Percent of change $=\frac{3,683}{116,278}\times 100$

  $\Rightarrow$ Percent of change $=\frac{368,300}{116,278}$

  $\Rightarrow$ Percent of change $=3.1674$

To the nearest tenth, the Percent of change is $3.2\%$ .

For city Columbus, OH

Amount of change = Final amount $-$ Original amount

  $\begin{array}{l}\Rightarrow A=733,203-711,470\\ \Rightarrow A=21,733\end{array}$

Therefore,

Percent of change $=\frac{21,733}{711,470}\times 100$

  $\Rightarrow$ Percent of change $=\frac{21,73300}{711,470}$

  $\Rightarrow$ Percent of change $=3.0546$

To the nearest tenth, the Percent of change is $3.1\%$ .

We got

For city Columbia, SC

Amount of change = $3,683$

Percent of change is $3.2\%$

For city Columbus, OH

Amount of change = $21,733$

Percent of change is $3.1\%$

On comparing both we get

Percent of change of Columbus and Columbia is almost same.

And both cities have Percent of increase.

Amount of change is different for Columbus and Columbia.