Ship taking on water: A ship collides with an iceberg at t = 0. One of...

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Ship taking on water: A ship collides with an iceberg at t = 0. One of the compartments of the ship, which is initially dry, starts to fill with water at a rate at, measured in liters per second, where t is time and a is a known constant. After a time t₁ the captain on the bridge switches on a pump which removes water at a known, constant rate ẞ, measured in liters per second. Compute the volume V(t) of water in the ship's compartment as a function of time t for all times. Ship taking on water: A ship collides with an iceberg at t = 0. One of the compartments of the ship, which is initially dry, starts to fill with water at a rate at, measured in liters per second, where t is time and a is a known constant. After a time t₁ the captain on the bridge switches on a pump which removes water at a known, constant rate ẞ, measured in liters per second. Compute the volume V(t) of water in the ship's compartment as a function of time t for all times.