I have several review word problems from differential equation class and. Hopefully can share (ask) with everyone in here.
1) a nitric acid solution flows at a constant rate of 6L/min into a large tank that initally held 200 L of 0.5% nitric acid solution. The solution inside the tank is kept well stirred and flows out of the tank at a rate of 8 L/min. if the solution entering the tank is 20% nitric acid, determine the volume of nitric acid in the tank after t min. When will the percentage of nitric acid in the tank reach 10%
2) Suppose that at a time t=0,5 thousand people in a city with population 40,000 people have heard a rumor. After 1 week the number P(t) of those who have heard it has increased to P(1)=8000. Assuming that P(t) satisfies a logistic equation, when will 60% of the city's population have heard the rumor?
3) A linear circuit has a resistance of 1 ohm, a capacitance of 0.5 farad a 2 volts battery. Find the current through the loop and the charge q(t) on the capacitor, given that initally there is no charge on the capacitor, q(0) = 0
4) It was noon on a cold December day in Tampa: 16 degree C. Detective Taylor arrived at the crime scence to find the sergent leaning over the body. The sergent said there were several suspects. If they knew the exact time of death, then they could narrow the list. Detective Taylor took out a thermometer and measured temperature of the body. 34.5 degree C. He then left for lunch. Upon returning at 1:00pm, He found the body temperature to be 33.7 degree C. When did the murder occur?
5) A compound C is formed when two chemicals A and B are combined. The resulting reaction between the two is such that for each gram of B, 2 grams of A are used. Initially there are 24grams of A and 18 grams of B. It is observed that 8 grams of the compound C are formed in 15 minutes. Determine the amount of C at any time if the rate of the reaction is proportional to the amounts of A and B remaining. Find the amount after 20 minutes.
6) A white wine at room temperature 70 degree F is chilled in ice (32F). If it take 15 minutes for the wine to chill to 60 degree F, how long will it take for the wine to reach 56 degree F?
thanks for your help.