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AP Calculus 7.4 Warm-Up 1) 12/8/15 Solve the differential equation. dy 1 4y 2 x 2 dx 2) Mathematician: A cup of coffee placed on a table cools at a rate of dH dt 0.05(H 70) degrees per minute, where H represents the temperature of the coffee and t is time in minutes. If the coffee was at 120ºF initially, what will its temperature be 10 minutes later? A) 73ºF B) 95ºF C) 100ºF D) 118ºF E) 143ºF AP Calculus §7.4 Separable Differentials Mathematician: 12/8/15 Solve the differential equation by separation of variables. (Mechanics) 1) dy y 5 x 2 dx 2) dy cos x e y sin x dx Solve the initial value problem by separation of variables. (Mechanics) 3) dy 2xy 2 dx and y 1 0.25 4) dy 4 y ln x dx x and y (e ) 1 5) The solution of the curve of A) y ex 3 B) y 2x 5 C) y 0.406e x D) y e x (e 2 3) y E) y' y that passes through the point (2,3) is: ex .406 (Application) 6) In some chemical reactions, the rate at which the amount of a substance changes with time is proportional to the amount present. For the change of glucono delta-lactone into gluconic acid, for example: dy 0.6y dt where t is measured in hours. If there are 100 grams of glucono delat-lactone present when t = 0, how many grams will there be left after the first hour? (Note: GDL is a naturally occurring food additive used as a preservative and commonly found in honey, fruit juices, and wine.) 7) The concentration of a medication injected into the bloodstream drops at a rate proportional to the existing concentration. If the factor of proportionality is 30% per hour, in how many hours will the concentration be one-tenth of the initial concentration? A) 3 B) 4 C) 6 D) 7 1 3 2 3 2 3