The mass of a biochemical sample MMM (measured in milligrams) varies over time ttt (measured in seconds, t>0t > 0t>0) according to a growth model. The mass-time curve passes through the point P(4,15)P(4, 15)P(4,15).
Given that
dMdt=5t2−402t \frac{\mathrm{d} M}{\mathrm{d} t} = \frac{5t^2 - 40}{2\sqrt{t}} dtdM=2t5t2−40Determine the equation of the tangent to the curve at the point PPP, writing your answer in the form M=kt+cM = kt + cM=kt+c, where kkk and ccc are integers to be found.
Find the function M(t)M(t)M(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.
