At 7 pm on a Wednesday evening. Mr Huxley's water tank was full. The capacity of the tank was 3 000 litres. Unfortunately, the tap on the tank was leaking in such a way that the change in volume at any time (f) hours was proportional to the volume (V) of the tank. AP =-kV. This means that dt (i) Show that =Ve* is a solution of this equation. (ii) Given that the volume of the tank after 3 hours is 1900 litres, show that k = 0.1523 correct to 4 decimal places. (i) By the time Mr Huxley discovered that the tank was leaking, there were only 250 litres of water remaining. At what time and on which day did Mr Huxley discover the leak (Answer correct to the nearest minute)?
At 7 pm on a Wednesday evening. Mr Huxley's water tank was full. The capacity of the tank was 3 000 litres. Unfortunately, the tap on the tank was leaking in such a way that the change in volume at any time (f) hours was proportional to the volume (V) of the tank. AP =-kV. This means that dt (i) Show that =Ve* is a solution of this equation. (ii) Given that the volume of the tank after 3 hours is 1900 litres, show that k = 0.1523 correct to 4 decimal places. (i) By the time Mr Huxley discovered that the tank was leaking, there were only 250 litres of water remaining. At what time and on which day did Mr Huxley discover the leak (Answer correct to the nearest minute)?
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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Transcribed Image Text:At 7 pm on a Wednesday evening. Mr Huxley's water tank was full.
The capacity of the tank was 3 000 litres.
Unfortunately, the tap on the tank was leaking in such a way that the change
in volume at any time (r) hours was proportional to the volume (V) of the
tank.
This means that
AP
=-kV .
dt
Show that V= Ve is a solution of this equation.
Given that the volume of the tank after 3 hours is 1900 litres, show that
k = 0.1523 correct to 4 decimal places.
(iii) By the time Mr Huxley discovered that the tank was leaking, there were
only 250 litres of water remaining.
At what time and on which day did Mr Huxley discover the leak
(Answer correct to the nearest minute)?
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