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 AQA A Level Maths 1.11 H: Integration with exam-style questions for A Level Maths. 436 questions covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only), matched to the AQA A Level Maths (7357) 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.
