Pollution. 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 P ( x ) = 2 x 1 − x 0 ≤ x < 1 where x is the percentage (expressed as a decimal fraction) of the total contaminant removed. (A) Where is P ( x ) increasing? Decreasing? (B) Where is the graph of P concave upward? Downward? (C) Find any horizontal or vertical asymptotes. (D) Find the x and y intercepts. (E) Sketch a graph of P .
Pollution. 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 P ( x ) = 2 x 1 − x 0 ≤ x < 1 where x is the percentage (expressed as a decimal fraction) of the total contaminant removed. (A) Where is P ( x ) increasing? Decreasing? (B) Where is the graph of P concave upward? Downward? (C) Find any horizontal or vertical asymptotes. (D) Find the x and y intercepts. (E) Sketch a graph of P .
Solution Summary: The author explains how the function P(x) is increasing or decreasing. The function is not defined when its denominator is 0. The domain can be divided into 2 intervals.
Pollution. 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
P
(
x
)
=
2
x
1
−
x
0
≤
x
<
1
where x is the percentage (expressed as a decimal fraction) of the total contaminant removed.
(A) Where is P(x) increasing? Decreasing?
(B) Where is the graph of P concave upward? Downward?
Do you have to be rich to invest in bonds and real estate? No, mutual fund shares are available to you even if you aren't rich. Let x represent annual percentage return (after expenses) on the Vanguard Total Bond Index Fund, and let y represent annual percentage return on the Fidelity Real Estate
Investment Fund. Over a long period of time, we have the following population estimates.
Hx = 7.34,
Ox = 6.55,
Hy = 13.15,
Oy = 18.55,
p z 0.424
(a) Do you think the variables x and y are independent? Explain your answer.
o Yes. Interest rate probably affects both investment returns.
o No. Interest rates probably has no effect on the investment returns.
o No. Interest rate probably affects both investment returns.
o Yes. Interest rates probably has no effect on the investment returns.
(b) Suppose you decide to put 60% of your investment in bonds and 40% in real estate. This means you will use a weighted average w = 0.6x + 0.4y. Estimate your expected percentage return uw and risk ow.
Pw =
Ow =…
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)= 14x
1−x
0≤x<1
(A) Where is P(x) increasing? Decreasing? 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 increasing on
...........
and decreasing on
..........…
Chapter 4 Solutions
Additional Calculus Topics for Calculus for Business, Economics, Life Sciences and Social Sciences
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