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Question 2 A tank is initially filled to capacity of 25 L with brine having a salt concentration of 5 g/L. Water containing 1 gL of salt is entering at a rate of 4 Lmin, and the mixture is allowed to flow out of the tank at a higher rate of 6 Limin. Find the concentration (in g/L) of salt in the tank when the amount of water left in the tank is half the initial amount.

Question 2 A tank is initially filled to capacity of 25 L with brine having a salt concentration of 5 g/L. Water containing 1 gL of salt is entering at a rate of 4 Lmin, and the mixture is allowed to flow out of the tank at a higher rate of 6 Limin. Find the concentration (in g/L) of salt in the tank when the amount of water left in the tank is half the initial amount.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Applications in Differential Equations (Growth and Decay, Newton's Cooling and Heating, Rate if Dissolution, and Mixing Problems) Question 1 A bacteria grows proportional to the square of its current population. Starting at an initial population of 200, its population doubles after 25 min. Calculate the additional time needed for its population to double again. Question 2 A tank is initially filed to capacity of 25 L with brine having a salt concentration of 5 g/L. Water containing 1 g/L of salt is entering at a rate of 4 L/min, and the mixture is allowed to flow out of the tank at a higher rate of 6 L/min. Find the concentration (in g/L) of salt in the tank when the amount of water left in the tank is half the initial amount. Question 3 A thermometer initially reading 100°C is placed in a liquid bath whose temperature is constant at 20°C. 6 min later, the temperature reading is 45°C. What would be its temperature reading after another 6 min? Question 4 The solubility of a certain salt in 100 g of water is 35 g. 25 g of the salt is placed in 80 g of water. If it takes 10 min to dissolve 10 g of the salt, calculate the additional time needed for another 10 g of salt to dissolve.
Transcribed Image Text:Applications in Differential Equations (Growth and Decay, Newton's Cooling and Heating, Rate if Dissolution, and Mixing Problems) Question 1 A bacteria grows proportional to the square of its current population. Starting at an initial population of 200, its population doubles after 25 min. Calculate the additional time needed for its population to double again. Question 2 A tank is initially filed to capacity of 25 L with brine having a salt concentration of 5 g/L. Water containing 1 g/L of salt is entering at a rate of 4 L/min, and the mixture is allowed to flow out of the tank at a higher rate of 6 L/min. Find the concentration (in g/L) of salt in the tank when the amount of water left in the tank is half the initial amount. Question 3 A thermometer initially reading 100°C is placed in a liquid bath whose temperature is constant at 20°C. 6 min later, the temperature reading is 45°C. What would be its temperature reading after another 6 min? Question 4 The solubility of a certain salt in 100 g of water is 35 g. 25 g of the salt is placed in 80 g of water. If it takes 10 min to dissolve 10 g of the salt, calculate the additional time needed for another 10 g of salt to dissolve.
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