2. A chemical reaction converts a certain chemical into another chemical, and the rate at which...

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2. A chemical reaction converts a certain chemical into another chemical, and the rate at which the first chemical is converted is proportional to the mount of chemical present at any time. At the end of one hour, 50 grams of the first chemical remain; while at the end of three hours, only 25 grams remain. dx(t) dt a) Solve the differential equation = -kx(t), with x(0) equal to the initial amount present and x(t) is the mount present at time t. b) How many grams of the first chemical were present initially? c) How many grams of the first chemical will remain after 5 hours? d) In how many hours will only 2 grams of the first chemical remain? 2. A chemical reaction converts a certain chemical into another chemical, and the rate at which the first chemical is converted is proportional to the mount of chemical present at any time. At the end of one hour, 50 grams of the first chemical remain; while at the end of three hours, only 25 grams remain. dx(t) dt a) Solve the differential equation = -kx(t), with x(0) equal to the initial amount present and x(t) is the mount present at time t. b) How many grams of the first chemical were present initially? c) How many grams of the first chemical will remain after 5 hours? d) In how many hours will only 2 grams of the first chemical remain?