Solution Found!
The incoming water has pollutant concentration c.t / D
Chapter , Problem 46(choose chapter or problem)
The incoming water has pollutant concentration \(\mathrm{c}(\mathrm{t})=10(1+\cos t)\mathrm{\ L}/\mathrm{m}^3\) that varies between 0 and 20, with an average concentration of 10 \(\mathrm{L} / \mathrm{m}^{3}\) and a period of oscillation of slightly over \(6 \frac{1}{4}\) months. Does it seem predictable that the lake's pollutant content should ultimately oscillate periodically about an average level of 20 million liters? Verify that the graph of x(t) does, indeed, resemble the oscillatory curve shown in Fig. 1.5.9. How long does it take the pollutant concentration in the reservoir to reach 10 \(L / m^{3}\)?
Questions & Answers
QUESTION:
The incoming water has pollutant concentration \(\mathrm{c}(\mathrm{t})=10(1+\cos t)\mathrm{\ L}/\mathrm{m}^3\) that varies between 0 and 20, with an average concentration of 10 \(\mathrm{L} / \mathrm{m}^{3}\) and a period of oscillation of slightly over \(6 \frac{1}{4}\) months. Does it seem predictable that the lake's pollutant content should ultimately oscillate periodically about an average level of 20 million liters? Verify that the graph of x(t) does, indeed, resemble the oscillatory curve shown in Fig. 1.5.9. How long does it take the pollutant concentration in the reservoir to reach 10 \(L / m^{3}\)?
ANSWER:
Step 1 of 4
Looking at equation (18)we conclude that the amount of pollutant 
Where 
