Chapter 4.2, Problem 24PPS

(a)

To determine

To Write:

A linear equation to find the cost C of a dictionary y years after 1904.

Answer to Problem 24PPS

The cost of dictionary after y years can be represented by the linear equation:

  $C=30+6y$

Explanation of Solution

Given Information:

In 1904, cost of a dictionary = 30 cent

Each year , cost of a dictionary rising = 6 cent

Formula Used:

The slope-intercept form of a line is:

  $\begin{array}{l}y=mx+b\mathrm{.....................................}(1)\\ where\\ m=slope\\ b=y-\mathrm{int}ercept\end{array}$

Calculation:

First , we form the equation :

Let y is the number of years since 1904

C is the cost of dictionary after y years

The C -intercept is 30 since the cost of a dictionary in the year y =0 ,1904 is 30

The slope is 6 since it represents the rate of increase in price

  $\begin{array}{l}m=6\\ b=30\\ \end{array}$

So, the equation of cost of dictionary after y years can be represented by:

Write the slope-intercept form by replacing ybyC and x by y :

  $\begin{array}{l}y=mx+b\mathrm{..............................}[slope-\mathrm{int}ercept]\\ C=6y+\mathrm{30............................}[y=C;x=y;b=30]\end{array}$

Hence, the cost of dictionary after y years from 1904 can be represented by the linear equation:

  $C=30+6y$

(b)

To determine

To Calculate:

If this trend continues, what will the cost of a dictionary be in 2020.

Answer to Problem 24PPS

If the trend continues, the cost of dictionary in the year 2020 will be 726 cent or $7.26

Explanation of Solution

Given Information:

From part (a), the cost of dictionary after y years from 1904 can be represented by the linear equation:

  $C=30+6y\mathrm{.............................}(2)$

Calculation:

Now, number of years from 1904 to 2020

  $\begin{array}{l}y=2020-1904\\ \Rightarrow y=116\\ Putting\_y=116\_in\_equation(2)\\ C=30+6(116)\\ \Rightarrow C=30+696\\ \Rightarrow C=726\end{array}$

Hence,

If the trend continues, the cost of dictionary in the year 2020 will be 726 cent or $7.26