Chapter 4.1, Problem 43PPS

(a)

To determine

To Calculate:

How many tons were sent to the landfill in 2010 .

Answer to Problem 43PPS

605.2 tons

Explanation of Solution

Given Information:

In 1998 , amount of waste sent to landfills = 946 tons.

Each year , reduced waste = 28.4 tons.

Calculation:

First , we form the equation :

Let x is the number of years since 1998

y is the tons sent to the landfill after x years

So, the equation of tons sent to the landfill after x years is given by:

  $y=946-28.4x\mathrm{......................}(1)$

Now, number of years from 1998 to 2010

  $\begin{array}{l}x=2010-1998\\ \Rightarrow x=12\\ Putting\_x=12\_in\_equation(1)\\ y=946-28.4(12)\\ \Rightarrow y=946-340.8\\ \Rightarrow y=605.2\end{array}$

(b)

To determine

To Calculate:

In what year will it become impossible for this trend to continue.

Answer to Problem 43PPS

2032

Explanation of Solution

Given Information:

In 1998 , amount of waste sent to landfills = 946 tons.

Each year , reduced waste = 28.4 tons.

Calculation:

First , we form the equation :

Let x is the number of years since 1998

y is the tons sent to the landfill after x years

So, the equation of tons sent to the landfill after x years is given by:

  $y=946-28.4x\mathrm{......................}(1)$

It will be impossible for the trend to continue when waste sent becomes 0.

That is , when y = 0.

Since no waste will be left to be sent to the landfills , so the trend will no longer continue. $$

Substituting y = 0 in equation (1)

  $\begin{array}{l}y=946-28.4x\mathrm{....................................}[y=0]\\ \Rightarrow 0=946-28.4x\\ \Rightarrow 28.4x=946-28.4x+28.4x\mathrm{............}[add"28.4x"both\_sides]\\ \Rightarrow 28.4x=946\\ \Rightarrow \frac{28.4x}{28.4}=\frac{946}{28.4}\mathrm{...................................}[divide"28.4"both\_sides]\\ \Rightarrow x=33.3\end{array}$

So, after 33 years since 1998 , the waste will become 0.

Hence,

  $\begin{array}{l}Year=1998+33\\ Year=2031\end{array}$

So, the waste will become 0 in 2031.

Hence, there will be nothing left to be sent to landfills after 2031. So, the trend will stop in the year 2032.