Date | May 2021 | Marks available | 6 | Reference code | 21M.1.AHL.TZ1.12 |
Level | Additional Higher Level | Paper | Paper 1 | Time zone | Time zone 1 |
Command term | Show that | Question number | 12 | Adapted from | N/A |
Question
A tank of water initially contains 400 litres. Water is leaking from the tank such that after 10 minutes there are 324 litres remaining in the tank.
The volume of water, V litres, remaining in the tank after t minutes, can be modelled by the differential equation
dVdt=-k√V, where k is a constant.
Show that V=(20-t5)2.
Find the time taken for the tank to empty.
Markscheme
dVdt=-kV12
use of separation of variables (M1)
⇒∫V-12 dV=∫-k dt A1
2V12=-kt A1
considering initial conditions A1
A1
A1
Note: Award A1 for any correct intermediate step that leads to the AG.
AG
Note: Do not award the final A1 if the AG line is not stated.
[6 marks]
minutes (M1)A1
[2 marks]