A tank is initially full of water. There is an open tap at the base of the tank which the water is draining out of. The height of water in the tank is h h\,h cm at time t t\,t seconds. The rate of change of the height of water is modelled as being directly proportional to the square root of the height of water.
When t=10t = 10t=10, h=36h = 36h=36 and, at this instant, the height is decreasing at a rate of 0.4 cms-1
Show that dhdt=−115h\displaystyle \frac{dh}{dt} = -\frac{1}{15}\sqrt{h}dtdh=−151h
Find an expression for h h\,h in terms of ttt.
Work out how long, according to the model, it takes for the tank to empty.
864 exam-style questions on Edexcel A Level Maths Integration, covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.