The mass MMM grams of a crystal growing in a chemical bath at time ttt hours is modelled by the differential equation
dMdt=10tMe2t,M≥0,t≥0 \frac{\text{d}M}{\text{d}t} = \frac{10t \sqrt{M}}{\text{e}^{2t}}, \quad M \ge 0, \quad t \ge 0 dtdM=e2t10tM,M≥0,t≥0Given that the initial mass of the crystal is 444 g, solve this differential equation to find an expression for M12M^{\frac{1}{2}}M21 in the form M12=f(t)M^{\frac{1}{2}} = f(t)M21=f(t).
Hence determine the equation of the horizontal asymptote to the curve with equation M12=f(t)M^{\frac{1}{2}} = f(t)M21=f(t).
Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions 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, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
