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In Silicon Valley, a number of computer firms were found to be contaminating underground water supplies with toxic chemicals stored in leaking underground containers. A water quality control agency ordered the companies to take immediate corrective action and contribute to a monetary pool for the testing and cleanup of the underground contamination. Suppose that the required monetary pool (in millions of dollars) is given by the following function, where \( x \) is the percentage (expressed as a decimal fraction) of the total contaminant removed. Complete parts (A) through (E). \( P(x)=\frac{11 x}{1-x} \quad 0 \leq x<1 \) B. \( P(x) \) is increasing on \( [0,1) \). \( P(x) \) is decreasing on C. Where is the graph of \( P \) concave upward? Downward? Select the correct choice below and fill in the answer box(es) to complete your choice. (Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) A. \( P(x) \) is concave upward on \( \square \) and concave downward on B. \( P(x) \) is concave upward on \( \square \) : C. \( P(x) \) is concave downward on \( \square \).

Ask by Bright Moreno. in the United States
Mar 17,2025

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\( P(x) \) is concave upward on \( [0, 1) \) and concave downward on no intervals.

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Beyond the Answer

First off, let’s explore the fascinating historical context of pollution regulation in the tech industry! During the late 20th century, environmental concerns became increasingly prominent, leading to stricter regulations on industrial waste disposal. The 1970s saw the birth of the Environmental Protection Agency (EPA) in the U.S., catalyzing initiatives to protect natural resources as companies faced legal repercussions for environmental violations. This set the stage for current practices in tech, where accountability has never been more crucial! Now, switching gears to real-world applications: the situation you described is a prime example of corporate responsibility in action! When tech companies contribute to a monetary pool for environmental cleanup, they not only protect local ecosystems but also enhance their public image, promoting sustainability. This helps foster consumer trust and can even influence investment opportunities; eco-conscious companies are often favored in today’s market! So, while those funds may seem like a burden, they ultimately pave the way for a healthier planet and better business.

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