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A large tank has a leak and the rate of change of the volume in the tank is given Question 18 by dV -kV? dt where t is time in minutes. Initially, the tank has 500 litres of water in it. 500 (a) Solve the differential equation and show that V = 1+ 500kt 1 (b) One minute later, a tenth of the water had leaked out. Show that k 4500 (c) Hence, find how long it takes for three quarters of the total water to leak out?

A large tank has a leak and the rate of change of the volume in the tank is given Question 18 by dV -kV? dt where t is time in minutes. Initially, the tank has 500 litres of water in it. 500 (a) Solve the differential equation and show that V = 1+ 500kt 1 (b) One minute later, a tenth of the water had leaked out. Show that k 4500 (c) Hence, find how long it takes for three quarters of the total water to leak out?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A large tank has a leak and the rate of change of the volume in the tank is given Question 18 by dV -kV? dt where t is time in minutes. Initially, the tank has 500 litres of water in it. 500 (a) Solve the differential equation and show that V = 1+ 500kt 1 (b) One minute later, a tenth of the water had leaked out. Show that k 4500 (c) Hence, find how long it takes for three quarters of the total water to leak out?
Transcribed Image Text:A large tank has a leak and the rate of change of the volume in the tank is given Question 18 by dV -kV? dt where t is time in minutes. Initially, the tank has 500 litres of water in it. 500 (a) Solve the differential equation and show that V = 1+ 500kt 1 (b) One minute later, a tenth of the water had leaked out. Show that k 4500 (c) Hence, find how long it takes for three quarters of the total water to leak out?
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