Chapter 5.1, Problem 31E

(a)

To determine

To find: The upper and lower estimate.

Answer to Problem 31E

Upper estimate: $\approx 60.9\text{ tons of pollutants}\text{.}$

Lower estimate: $\approx 46.8\text{ tons of pollutants}\text{.}$

Explanation of Solution

Given information:

The table is:

  

Calculation:

Because the pace at which pollutants are released is growing, an upper estimate of the total tonnage of pollutants is provided using data from the end of each month.

Upper estimate:

  $\begin{array}{c}30\times (0.20+0.25+0.27+0.34+0.45+0.52)\\ \approx 60.9\text{ tons of pollutants}\text{. }\end{array}$

Because the pace at which pollutants are released is growing, a lower estimate of the total tonnage of pollutants is produced using data from the previous month's end. Although  don't have any data for the first of January,  know that pollutants were emitted at a rate of $0.05\text{ ton/day}$ for new scrubbers. Therefore,

Lower estimate:

  $\begin{array}{c}30\times (0.05+0.20+0.25+0.27+0.34+0.45)\\ \approx 46.8\text{ tons of pollutants}\text{. }\end{array}$

Therefore the required upper estimate: $\approx 60.9\text{ tons of pollutants}\text{.}$

Lower estimate: $\approx 46.8\text{ tons of pollutants}\text{.}$

(b)

To determine

To find: The time when a total of $\text{125}$ tons will have been released into the atmosphere.

Answer to Problem 31E

Explanation of Solution

Given information:

The table is:

  

Calculation:

To use the left rectangles, the amount of pollutants discharged by the end of October is:

  $\begin{array}{c}30\times (0.05+0.20+0.25+0.27+0.34+0.45+0.52+0.63+0.70+0.81)\\ =126.6\text{ tons}\text{. }\end{array}$

Therefore the required by the end of October, a total of $\text{125}$ tons will have been released into the atmosphere.