Math 1B Quiz 10 Thursday 8 November 2007 GSI Theo Johnson Freyd http math berkeley edu theojf Name 1 3 pts Show that f t Cet t 1 is a one parameter family of solutions to the differential equation df f t t dt If f 0 1 what is f t 1 2 3 pts Which of the three direction fields corresponds to the differential equation df f 1 f 2 dt Each is graphed with f and t ranging from 3 to 3 Based on the graph or any other way specify which values of f are equilibrium values Which of these equilibria are stable and which are unstable as t Sketch the solution to this differential equation that satisfies the initial value condition that f 0 when t 0 2 3 4 pts Set up but do not solve a differential equation modeling the following rather unlikely situation Be sure to specify the meanings of your symbols you should provide a dictionary that translates the interesting quantities into your chosen variables h height for instance Also be sure to specify the initial condition for the problem Dr Gregory House s evil twin Dr Geoffrey Condo breaks into the set of Grey s Anatomy hoping to murder his brother s arch rival Dr Meredith Grey He successfully restrains her to a hospital bed and implants her with an intravenous drug drip which he programs to administer an increasing supply of painkillers 100 miligrams this hour then 200 mg and so on so that the input rate of painkiller is proportional to the amount of time since she was incapacitated Dr Condo hopes that by doing this Dr Grey will overdose on painkillers But Dr Grey s kidneys decide to try to keep her from dying and filter out the painkiller assuming the IV also administers plenty of water at the right salinity In particular in an hour her kidneys can filter out one tenth of the total painkillers in her body How much painkiller is in Dr Grey s body after a given amount of time 3
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