An oil tank contains 100 liters of oil an initial time t = 0. Someone starts pumping oil into the tank at a constant rate of 10 liters per second. Simultaneously, oil starts flowing out through the outlet in the base at the rate ț² (in liters per second) at time t. a. Find the differential equation that would describe the volume of the oil in the tank at time t (in seconds). b. Find the volume of the oil in the tank at time t (in seconds). c. Will the tank ever be empty? Explain.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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I tried related rates for this one, but the answer is really weird. (Should I do related rates or I should do optimization? But the f''(x) test was concave down). Thank you for helping!

An oil tank contains 100 liters of oil an initial time t = 0. Someone starts pumping oil into the tank
at a constant rate of 10 liters per second. Simultaneously, oil starts flowing out through the outlet in
the base at the rate £² (in liters per second) at time t.
a. Find the differential equation that would describe the volume of the oil in the tank at time t (in
seconds).
b. Find the volume of the oil in the tank at time t (in seconds).
c. Will the tank ever be empty? Explain.
Transcribed Image Text:An oil tank contains 100 liters of oil an initial time t = 0. Someone starts pumping oil into the tank at a constant rate of 10 liters per second. Simultaneously, oil starts flowing out through the outlet in the base at the rate £² (in liters per second) at time t. a. Find the differential equation that would describe the volume of the oil in the tank at time t (in seconds). b. Find the volume of the oil in the tank at time t (in seconds). c. Will the tank ever be empty? Explain.
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