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14. a. The decay of a particular fruit with total mass, M, satisfies the following differential equation: dᎷ dt -k M3/4 M(0) = 16 g, where t is in days. It is found that after 10 days only 1 g remains of the fruit, so M(10) = 1. Solve this differential equation. Find the value of k. Determine when the fruit completely vanishes (M(tf) = 0). b. A special culture of bacteria is added to the decaying fruit, and it is found that the decaying fruit satisfies the differential equation: dM dt = -0.8e-0.024 M3/4, M(0) = 16 g, = Solve this differential equation. Find the length of time for this fruit to completely vanish.