MATH 307 Midterm: MATH 307 UW 307 Su10 SolA
Document Summary
Math 307, sections a, b and c, summer 2010, solutions to final exam: consider a reservoir with a volume of 9 billion cubic meters and an initial pollutant concentration of. There is a daily in ow of 450 million cubic meters of water with a pollutant concentration of 0. 05% and an equal daily out ow of the well-mixed water. Let p (t) be the amount of contaminant in cubic meters at time t in days. = 450 106 0. 05 10 2 . 9 109 p, p (0) = 0. 25 10 2 9 109 or dp dt. = 22. 5 104 0. 05p, p (0) = 2. 25 107. 1 e0. 05t z 22. 5 104e0. 05tdt = 45 105 + ce 0. 05t solving for c from the initial condition. P (t) = 45 105 + 180 105e 0. 05t so. 13. 86days: use the laplace table to answer the following questions. (a) find the inverse laplace transform of.
