Chapter 4.1, Problem 43PPS

a.

To determine

To find:Number of tons of waste sent to land fil in 2016.

Answer to Problem 43PPS

Waste sent to landfill in 2016 is 605.2 tons

Explanation of Solution

Given information:

Table which represents the amount of wastage in tons since 2004( $t=0$ )

we need to write a function wastage in terms of time (in years).

Let wastage be $\text{'}y\text{'}$ and time be $\text{'}t\text{'}$

Let us assume

  $y=at+b$

Here $a,b$ are constants.

Put point $\left(0,946\right)$ in above equation

We get

  $\Rightarrow 946=a\left(0\right)+b$

  $\Rightarrow b=946$ .

Substitute point $\left(5,804\right)$

We get

  $\begin{array}{l}\Rightarrow 804=a\left(5\right)+b\\ \Rightarrow 804=5a+946\\ \Rightarrow 5a=804-946\\ \Rightarrow 5a=-142\\ \Rightarrow a=-28.4\end{array}$

Therefore

  $y=-28.4t+946$

Substitute point $\left(10,662\right)$

We get

  $\begin{array}{l}\Rightarrow 662=-28.4(10)+946\\ \Rightarrow 662=-284+946\\ \Rightarrow 662=662\end{array}$

So, Point (10,662) is satisfying

So, the assumption we made $y=at+b$ is correct.

Therefore

  $y=-28.4t+946$

Where

  $y=$ wastage in tons

  $t=$ time in years

put $t=12$ it means 12 years from 2004 that is 2016

  $\begin{array}{l}y=-28.4t+946\\ \Rightarrow y=-28.4(12)+946\\ \Rightarrow y=-340.8+946\\ \Rightarrow y=605.2\end{array}$

Therefore

Waste sent to landfill in 2016 is 605.2 tons.

b.

To determine

To find: In which year it is impossible to continue this trend.

Answer to Problem 43PPS

After 33.3 years this trend will be impossible

Explanation of Solution

Given information:

Table which represents the amount of wastage in tons since 2004( $t=0$ )

Maximum reduction of wastage is zero.

So put y=0

We get

  $\begin{array}{l}y=-28.4t+946\\ \Rightarrow 0=-28.4(t)+946\\ \Rightarrow 28.4t=946\\ \Rightarrow t=\frac{946}{28.4}\\ \Rightarrow t=33.3\end{array}$

So, after 33.3 years this trend will be impossible.