SUPPLEMENTARY HOMEWORK FOR WEEK 5 MATH2573H, SPRING 2012, UNIVERSITY OF MINNESOTA Summary: SUPPLEMENTARY HOMEWORK FOR WEEK 5 MATH2573H, SPRING 2012, UNIVERSITY OF MINNESOTA GREG W. ANDERSON Salt tank problem A large tank initially contains 240 gallons of water and 35 pounds of salt. At time t = 0 brine begins to flow into the tank at a rate of 4 gal/min. The brine contains salt at a concentration of 4 pounds per gallon. Well-mixed solution is allowed to drain from the tank at a rate of 7 gal/min. Find the amount of salt in the tank at time t (until the tank runs dry). Coroner's report A body is discovered in a park at 3am in the morning. All through the evening the temperature is a steady 45o Fahrenheit. The temperature of the body is mea- sured at 3am and again at 4am just before moving the body to the morgue. The temperatures are 80o and 60o Fahrenheit, respectively. Estimate the time of death using Newton's law of heating/cooling. Start with the differential equation. Logistic equation Find the general solution of the differential equation Collections: Mathematics