Chapter 1.1, Problem 45E

a.

To determine

To calculate the minimum wages.

Answer to Problem 45E

Decade $2000$ to $2010$

Explanation of Solution

Given information:

Use the graph below, which shows the minimum wages in the United States (in dollars) from $1950$ through $2011$ .

  

Which decade shows the greatest increase in minimum wage?

Calculation:

The graph shows the minimum wages in the United States (in dollars) from $1950$ through $2011$ .

The greatest increase in minimum wages $2000$ to $2010$

The graph show wages in $2000$ is $\$5.1$

The graph show wages in $2010$ is $\$7.2$

Therefore the increase in minimum wages is,

  $\$7.2-\&5.1=\$2.1$

Hence the decade $2000$ to $2010$ shows the greatest increase in minimum wages.

b.

To determine

To calculate the minimum wages.

Answer to Problem 45E

  $\boxed{11.8\%}$

  $\boxed{70.6\%}$

Explanation of Solution

Given information:

Use the graph below, which shows the minimum wages in the United States (in dollars) from $1950$ through $2011$ .

  

Approximate the percent increases in the minimum wage from 1990 to 1995 and from 1995 to 2011.

Calculation:

The graph shows the minimum wages in $1990$ is approximately $3.8$ and $1995$ is $4.25$

So, % age increase in wages is.

  $\begin{array}{l}\frac{wages1995-wages1990}{wages1990}\times 100\\ =\frac{4.25-3.8}{3.8}\times 100\\ =11.841205\\ =11.8\end{array}$

Hence % age increase from $1990$ to $1995$ is $\boxed{11.8\%}$ .

Similarly the minimum wages in $1995$ is $4.25$ and in $2011$ are $7.25$ .

So, % age increase in wages is.

  $\begin{array}{l}\frac{wages2011-wages1995}{wages1990}\times 100\\ =\frac{7.25-4.25}{4.25}\times 100\\ =70.588235\\ =70.6\end{array}$

Hence % age increase from $1995$ to $2011$ is $\boxed{70.6\%}$ .

c.

To determine

To calculate the minimum wages.

Answer to Problem 45E

The predict wages in $2016$ is $\$12.3685$

Explanation of Solution

Given information:

Use the graph below, which shows the minimum wages in the United States (in dollars) from $1950$ through $2011$ .

  

Use the percent increase from 1995 to 2011 to predict the minimum wage in 2016.

Calculation:

From part (b) the %age increase from $1995$ to $2011$ is $70.6\%$ , use minimum wage in $2016$ would be wages in $2011$ that is $\$7.2$ plus $70.6\%$ of $\$7.2$ .

So,

  $\begin{array}{l}7.25+7.25\times 70.6\%=7.25+7.25\times \frac{70.6}{100}\\ =7.25+7.25\times 0.706\\ =12.3685\end{array}$

Hence predict wages in $2016$ is $\$12.3685$

d.

To determine

To calculate the minimum wages.

Answer to Problem 45E

Prediction is not reasonable

Explanation of Solution

Given information:

Use the graph below, which shows the minimum wages in the United States (in dollars) from $1950$ through $2011$ .

  

Do you believe that your prediction in part (c) is reasonable? Explain

Calculation:

No the prediction in part C) is not reasonable.

It is too high because %age increase over a seven year period ( $2009-2016$ ) is less than %age increase over a $16$ year period ( $1995$ to $2011$ )

Hence prediction is not reasonable.