Your swimming pool containing 80000 gal of water has been contaminated by 8 kg of a nontoxic dye that leaves a swimmer's skin an unattractive green. With your filter pump running at 250 gal/min to clear the dye, the function q(t)=6000et/320 gives the amount of dye (in grams) in the pool at any time t (in minutes). You have invited several dozen friends to a pool party that is scheduled to begin in 6 hours. You have determined that the effect of the dye is imperceptible if its concentration is less than 0.02 g/gal. (c) Is your filtering system capable of reducing the dye concentration to this level within 6 hours? The filtering system (choose: is is not) capable of reducing the dye concentration to this level in the given amount of time. (d) Find the time T at which the concentration of the dye first reaches the value of 0.02 g/gal. Note: round your answer to two decimal places T = hours r (e) Find the flow rate that is sufficient to achieve the concentration 0.02 g/gal within 4 hours. Note: round your answer to the nearest integer. ______gallons/min r =
Your swimming pool containing 80000 gal of water has been contaminated by 8 kg of a nontoxic dye that leaves a swimmer's skin an unattractive green. With your filter pump running at 250 gal/min to clear the dye, the function q(t)=6000et/320 gives the amount of dye (in grams) in the pool at any time t (in minutes). You have invited several dozen friends to a pool party that is scheduled to begin in 6 hours. You have determined that the effect of the dye is imperceptible if its concentration is less than 0.02 g/gal. (c) Is your filtering system capable of reducing the dye concentration to this level within 6 hours? The filtering system (choose: is is not) capable of reducing the dye concentration to this level in the given amount of time. (d) Find the time T at which the concentration of the dye first reaches the value of 0.02 g/gal. Note: round your answer to two decimal places T = hours r (e) Find the flow rate that is sufficient to achieve the concentration 0.02 g/gal within 4 hours. Note: round your answer to the nearest integer. ______gallons/min r =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Your swimming pool containing 80000 gal of water has been
contaminated by 8 kg of a nontoxic dye that leaves a swimmer's
skin an unattractive green. With your filter pump running at 250
gal/min to clear the dye, the function q(t)=6000et/320 gives the
amount of dye (in grams) in the pool at any time t (in minutes).
You have invited several dozen friends to a pool party that is
scheduled to begin in 6 hours. You have determined that the
effect of the dye is imperceptible if its concentration is less than
0.02 g/gal.
(c) Is your filtering system capable of reducing the dye
concentration to this level within 6 hours?
The filtering system (choose: is is not) capable of
reducing the dye concentration to this level in the given amount
of time.
(d) Find the time T at which the concentration of the dye first
reaches the value of 0.02 g/gal.
Note: round your answer to two decimal places
T =
hours
r
(e) Find the flow rate that is sufficient to achieve the
concentration 0.02 g/gal within 4 hours.
Note: round your answer to the nearest integer.
______gallons/min
r =
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