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).
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.