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3. Determine the half-life of the radioactive substance in the previous problem.

3. Determine the half-life of the radioactive substance in the previous problem.

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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§1.11 - APPLICATIONS OF 1ST ORDER EQUATIONS APPLICATIONS OF 1ST ORDER EQUATIONS are presented in §3.2 and §3.3 of the Zill text. 1. The population of a town grows at a rate proportional to the population at time t. Its initial population of 500 increases by 15% in 10 years. What will be the population in 30 years? PROBLEM SET 1.11 2. Initially, there were 100 milligrams of a radioactive substance. After 6 hours, the mass had decreased by 3%. If the rate of decay is proportional to the amount of the substance present at time t, find the amount remaining after 24 hours. 3. Determine the half-life of the radioactive substance in the previous problem. 4. A thermometer is taken from an inside room where the air temperature is 70°F to the outside where the air temperature is 10°F. After a minute, the thermometer reads 50°F. What is the reading at t = 1 minute? How long will it take for the thermometer to reach 15°F? 5. A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pumped into a tank at a rate of 4 liters per minute; the well-mixed solution is pumped out at the same rate. Find the number of grams of salt A(t) in the tank at time t. 6. A large tank is filled with 500 gallons of pure water. Brine containing 2 pounds of salt per gallon is pumped into the tank at a rate of 5 gallons per minute. The well-mixed solution is pumped out at the same rate. Find the number of pounds of salt A(t) in the tank at time t. 7. Solve Problem 6 under the assumption that the solution is pumped out at a faster rate of 10 gallons per minute. When is the tank empty? 8. A large tank is partially filled with 100 gallons in which 10 pounds of salt is dissolved. Brine containing lb of salt per gallon is pumped into the tank at a rate of 6 gallons per minute. The
Transcribed Image Text:§1.11 - APPLICATIONS OF 1ST ORDER EQUATIONS APPLICATIONS OF 1ST ORDER EQUATIONS are presented in §3.2 and §3.3 of the Zill text. 1. The population of a town grows at a rate proportional to the population at time t. Its initial population of 500 increases by 15% in 10 years. What will be the population in 30 years? PROBLEM SET 1.11 2. Initially, there were 100 milligrams of a radioactive substance. After 6 hours, the mass had decreased by 3%. If the rate of decay is proportional to the amount of the substance present at time t, find the amount remaining after 24 hours. 3. Determine the half-life of the radioactive substance in the previous problem. 4. A thermometer is taken from an inside room where the air temperature is 70°F to the outside where the air temperature is 10°F. After a minute, the thermometer reads 50°F. What is the reading at t = 1 minute? How long will it take for the thermometer to reach 15°F? 5. A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pumped into a tank at a rate of 4 liters per minute; the well-mixed solution is pumped out at the same rate. Find the number of grams of salt A(t) in the tank at time t. 6. A large tank is filled with 500 gallons of pure water. Brine containing 2 pounds of salt per gallon is pumped into the tank at a rate of 5 gallons per minute. The well-mixed solution is pumped out at the same rate. Find the number of pounds of salt A(t) in the tank at time t. 7. Solve Problem 6 under the assumption that the solution is pumped out at a faster rate of 10 gallons per minute. When is the tank empty? 8. A large tank is partially filled with 100 gallons in which 10 pounds of salt is dissolved. Brine containing lb of salt per gallon is pumped into the tank at a rate of 6 gallons per minute. The
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Given: The radioactive substance was 100 milligrams initially. The mass is decreased by 3% after 6 hours. The rate of decay is proportional to the amount of the substance present at the time t.

To find: The half-life of the radioactive substance.

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