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Assume that the rate at which a population of a country grows is proportional to the total population at that time with a constant immigration rate of r > 0. Write a differential equation used to find the population P(t). (You do not need to solve this differential equation.)

Assume that the rate at which a population of a country grows is proportional to the total population at that time with a constant immigration rate of r > 0. Write a differential equation used to find the population P(t). (You do not need to solve this differential equation.)

Advanced Engineering Mathematics
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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1. Assume that the rate at which a population of a country grows is proportional to the total population at that time with a constant immigration rate of r > 0. Write a differential equation used to find the population P(t). (You do not need to solve this differential equation.) 2. A can of soda at 40°F is placed into a room where the temperature is 70°F. Assume that Newton's Law of Cooling/Warming applies: The rate of cooling/warming is proportional to the difference between the current temperature and the ambient temperature. Let T represent the current temperature of the soda at time, t, in minutes. Write an initial-value problem used to find the temperature of the soda. (You do not need to solve this initial-value problem.) 3. A 10 gallon tank is filled with 10 gallons of water in which 3 pounds of salt is dissolved. A mixture containing a solution with 1 pound per gallon begins flowing into the tank at a rate of 2 gal/min. Simultaneously, a drain is opened at the bottom of the tank allowing the solution to leave the tank at a rate of 2 gal/min. Write an initial-value problem used to find the amount of salt in the tank. (You do not need to solve this initial-value problem.)
Transcribed Image Text:1. Assume that the rate at which a population of a country grows is proportional to the total population at that time with a constant immigration rate of r > 0. Write a differential equation used to find the population P(t). (You do not need to solve this differential equation.) 2. A can of soda at 40°F is placed into a room where the temperature is 70°F. Assume that Newton's Law of Cooling/Warming applies: The rate of cooling/warming is proportional to the difference between the current temperature and the ambient temperature. Let T represent the current temperature of the soda at time, t, in minutes. Write an initial-value problem used to find the temperature of the soda. (You do not need to solve this initial-value problem.) 3. A 10 gallon tank is filled with 10 gallons of water in which 3 pounds of salt is dissolved. A mixture containing a solution with 1 pound per gallon begins flowing into the tank at a rate of 2 gal/min. Simultaneously, a drain is opened at the bottom of the tank allowing the solution to leave the tank at a rate of 2 gal/min. Write an initial-value problem used to find the amount of salt in the tank. (You do not need to solve this initial-value problem.)
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