2. [011 Points] DETAILS PREVIOUS ANSWERS ZILLDIFFEQMODAP11 1.3.002. MY NOTES ASK YOUR TEACHER The population model given in (1) in Section 1.3 . P or f = 1:.\" (1) dt or fails to take death into consideration; the growth rate equals the birth rate. In another model of a changing population of a community it is assumed that the rate at which the population changes is a net ratethat is, the difference between the rate of births and the rate of deaths in the community. Determine a model for the population PM if both the birth rate and the death rate are proportional to the population present at time t a 0. [Assume the constants of proportionality for the birth and death rates are k1 and k2 respectively. Use Pfor Pm.) %='k1-pk2-p= (k1k2)p x Need Help? 7. [GM Points] DETAILS PREVIOUS ANSWERS ZILLDIFFEQMODAPH 1.3.01 O.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Suppose that a large mixing tank initially holds 500 gallons of water in which 50 pounds of salt have been dissolved. Another brine solution is pumped into the tank at a rate of 3 gal/min, and when the solution is well stirred, it is then pumped out at a slower rate of 2 gelxmin. If the concentration of the solution entering is 2 Ib/gal, determine a differential equation (in Ibfmin) for the amount of salt A\") (in lb) in the tank at time t > 0. (Use A for A(t).) Need Help? 8. [015 Points] DETAILS PREVIOUS ANSWERS ZILLDIFFEQMODAP11 1.3.010.M|.SA. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER This question has several parts that must be compieted sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped pant. _utoria| Exercise Suppose that a large mixing tank initially holds 600 gallons of water in which 50 pounds of salt have been dissolved. Another brine solution is pumped into the tank at a rate of 3 gal/min, and when the solution is well stirred, it is then pumped out at a slower rate of 2 galfmin. If the concentration of the solution entering is 3 lb/gal, determine a differential equation for the amount of salt A(t) in the tank at time t > 0. We are told that a large mixing tank contains 600 gallons of water in which 50 pounds of salt has been dissolved, known as a brine solution. A brine solution with a different concentration of salt is added to the tank at a constant rate, while solution is also being removed from the tank at different constant rate. It is described that the solution is pumped out after the solution is well stirred. This is meant to assure us that the system has the ideal conditions that as the one solution is added to the tank, the concentration of the salt in the solution in the tank is perfectly uniform. We are asked to determine a differential equation for the amount of salt A(t) in the bank at time t > 0. We are told that the new brine solution is added to the tank at the rate of 3 gal/min and that the concentration of salt is 3 lb/gal. Therefore, the rate that salt is added to the tank {in lb/min) is the product of the rate of the solution that is added to the tank and the concentration of the salt in the added solution. Rm = (3 gal/min) - (3 lb/gal) = x lbfmin I Submit H Skip (you cannotcome back} l