The surface area SSS (measured in cm2\text{cm}^2cm2) of a particular fungus culture is observed over time ttt (measured in hours). The growth of the culture is modeled by the differential equation
dSdt=8tS1/2e2t,S≥0,t≥0 \frac{\text{d}S}{\text{d}t} = \frac{8t S^{1/2}}{\text{e}^{2t}}, \quad S \ge 0, \quad t \ge 0 dtdS=e2t8tS1/2,S≥0,t≥0Given that the initial surface area of the fungus is 9 cm2 at t=0t = 0t=0, solve this differential equation to find S1/2S^{1/2}S1/2 in terms of ttt, giving your answer in the form S1/2=g(t)S^{1/2} = g(t)S1/2=g(t).
Hence find the equation of the horizontal asymptote to the curve with equation S1/2=g(t)S^{1/2} = g(t)S1/2=g(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.
