Recent technological breakthroughs now allow greenhouses in Ontario to grow tomatoes during winter in Canada. A gardener in one of these greenhouse was dissolving dry nutrients into a large hydroponic tank, which initially held 200 L of water. While rushing, they realized they unfortunately added too much of the dry nutrients, so that the concentration in the tank is now 5 grams per litre. Because all the nutrients are already dissolved, so that the solution is well mixed, they now begin adding freshwater (without any additional nutrients) to the tank at a rate of 3 litres per minute, while also opening a valve that lets water flow out at a rate of 2 litres per minute. Assume the tank is large enough such that it will not overflow during the remainder of this question. (a) Let N(t) be the amount of nutrient in the tank at time t. For how long should the gardener keep the water flowing in and the outflow valve open to bring the concentration to 2 grams per litre? (b) The gardener now realizes the water flowing in also, unexpectedly, contained some of the nutrient, at a concentration of 1 gram per litre. How much longer do they need to keep the water flowing in and the outflow value open to reach 2 grams per litre?
Recent technological breakthroughs now allow greenhouses in Ontario to grow tomatoes during winter in Canada. A gardener in one of these greenhouse was dissolving dry nutrients into a large hydroponic tank, which initially held 200 L of water. While rushing, they realized they unfortunately added too much of the dry nutrients, so that the concentration in the tank is now 5 grams per litre. Because all the nutrients are already dissolved, so that the solution is well mixed, they now begin adding freshwater (without any additional nutrients) to the tank at a rate of 3 litres per minute, while also opening a valve that lets water flow out at a rate of 2 litres per minute. Assume the tank is large enough such that it will not overflow during the remainder of this question. (a) Let N(t) be the amount of nutrient in the tank at time t. For how long should the gardener keep the water flowing in and the outflow valve open to bring the concentration to 2 grams per litre? (b) The gardener now realizes the water flowing in also, unexpectedly, contained some of the nutrient, at a concentration of 1 gram per litre. How much longer do they need to keep the water flowing in and the outflow value open to reach 2 grams per litre?
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:Recent technological breakthroughs now allow greenhouses in Ontario to grow tomatoes during winter
in Canada. A gardener in one of these greenhouse was dissolving dry nutrients into a large hydroponic tank,
which initially held 200 L of water. While rushing, they realized they unfortunately added too much of the dry
nutrients, so that the concentration in the tank is now 5 grams per litre. Because all the nutrients are already
dissolved, so that the solution is well mixed, they now begin adding freshwater (without any additional nutrients)
to the tank at a rate of 3 litres per minute, while also opening a valve that lets water flow out at a rate of 2
litres per minute. Assume the tank is large enough such that it will not overflow during the remainder of this
question.
(a) Let N(t) be the amount of nutrient in the tank at time t. For how long should the gardener keep the water
flowing in and the outflow valve open to bring the concentration to 2 grams per litre?
(b) The gardener now realizes the water flowing in also, unexpectedly, contained some of the nutrient, at a
concentration of 1 gram per litre. How much longer do they need to keep the water flowing in and the
outflow value open to reach 2 grams per litre?
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