Chapter 4.1, Problem 60PPS

(a)

To determine

To find:The equation that represents the circulation caftery years.

Answer to Problem 60PPS

The equation that represents the cost C of a membership for m monthsis

  $c=33,388y+500,000$ .

Explanation of Solution

Given:

The initial circulation is500,000.

The increment rate of the circulation = $\text{33,388 per year}$

Calculation:

The standard form of slope and intercept form of the straight line is $y=mx+c$ .

Here m is the slope of the straight line and c is the y- intercept of the equation.

The initial circulation is the intercept of the line on the y- axis while the increment rate is the slope of the equation.

Write the equation for the given situation.

Substitute $33,388$ for slope m and $500,000$ for y- intercept c .

The equation of the straight line in the slope and intercept form is

  $c=33,388y+500,000$

Here, y is the number of years.

Therefore, the equation of the straight line is $c=33,388y+500,000$ .

(b)

To determine

To find:The meaning of slope in equation.

Answer to Problem 60PPS

The slope in the equation represents the rate of increase of the circulation of magazine with years.

Explanation of Solution

Given:

The initial circulation is 500,000.

The increment rate of the circulation = $\text{33,388 per year}$

Calculation:

The standard form of slope and intercept form of the straight line is $y=mx+c$ .

Here m is the slope of the straight line and c is the y- intercept of the equation.

The initial circulation is the intercept of the line on the y- axis while the increment rate is the slope of the equation.

Write the equation for the given situation.

Substitute $33,388$ for slope m and $500,000$ for y- intercept c .

The equation of the straight line in the slope and intercept form is

  $c=33,388y+500,000$

Here, y is the number of years. The slope of the equation is 33.388 which represents the rate of increase of circulation of magazine over y -years.

Therefore, the equation of the straight line is $c=33,388y+500,000$ and the slope of the equation represents the rate of increase of circulation of magazine over y -years.

.

(c)

To determine

To find:The meaning of C intercept in equation.

Answer to Problem 60PPS

The intercept of the equation is 500,000 which represents the circulation of the magazine in the first year.

Explanation of Solution

Given:

The initial circulation is 500,000.

The increment rate of the circulation = $\text{33,388 per year}$

Calculation:

The standard form of slope and intercept form of the straight line is $y=mx+c$ .

Here m is the slope of the straight line and c is the y- intercept of the equation.

The initial circulation is the intercept of the line on the y- axis while the increment rate is the slope of the equation.

Write the equation for the given situation.

Substitute $33,388$ for slope m and $500,000$ for y- intercept c .

The equation of the straight line in the slope and intercept form is

  $c=33,388y+500,000$

Here, y is the number of years. The intercept of the equation is 500,000 which represents the circulation of the magazine in the first year. This circulation of the magazine in the first year is independent of variations over time.

Therefore, the equation of the straight line is $c=33,388y+500,000$ and the C intercept of the equation represents the circulation of the magazine in the first year.

(d)

To determine

To find:The year in which circulation reaches 3,000,000.

Answer to Problem 60PPS

The circulation reaches 3 million in the year 2019.

Explanation of Solution

The initial circulation is 500,000.

The increment rate of the circulation = $\text{33,388 per year}$

Calculation:

The standard form of slope and intercept form of the straight line is $y=mx+c$ .

Here m is the slope of the straight line and c is the y- intercept of the equation.

The initial circulation is the intercept of the line on the y- axis while the increment rate is the slope of the equation.

Write the equation for the given situation.

Substitute $33,388$ for slope m and $500,000$ for y- intercept c .

The equation of the straight line in the slope and intercept form is

  $c=33,388y+500,000$

Here, y is the number of years. Substitute 3,000,000 for c in the equation and calculate the value of y .

  $\begin{array}{l}3,000,000=33,388y+500,000\\ y=\frac{3,000,000-500,000}{33,388}\\ =74.877\sim 75\text{ years}\end{array}$

The magazine began in the year 1944 and it takes 75 years to reach the circulation to 3,000,000. Thus, the circulation reaches 3 million in $1944+75=2019$ .

Therefore, the circulation reaches 3,000,000 in the year 2019.