Question

The percent p of particulate pollution that can be removed from the smokestacks of an industrial plant by spending C dollars is given by the following equation. 100C p = 5700 +C Find the percent of the pollution that could be removed if spending C were allowed to increase without bound. Can 100% of the pollution be removed? Explain. 100% of the pollution can be removed. There is a limited cost. 100% of the pollution cannot be removed. The cost would be impossible to afford.

Answer 1

we are given equation as

$p=\frac{100C}{5700+C}$

we can find limit

$\lim_{C-->\infty}p=\lim_{C-->\infty}\frac{100C}{5700+C}$

$\lim_{C-->\infty}p=\lim_{C-->\infty}\frac{100C/C}{5700/C+C/C}$

$\lim_{C-->\infty}p=\lim_{C-->\infty}\frac{100}{5700/C+1}$

$\lim_{C-->\infty}p=\frac{100}{0+1}$

$\lim_{C-->\infty}p=100$ ..............Answer