The population of a luminescent algae colony, PPP, measured in thousands, is modelled by the function
P(t)=4t−20t+25,t>0 P(t) = 4t - 20\sqrt{t} + 25, \quad t > 0 P(t)=4t−20t+25,t>0where ttt is the time in hours since the colony was first observed.
Determine the values of ttt for which the population is exactly 9 thousand.
Find the value of ttt for which d2Pdt2=527\dfrac{d^2P}{dt^2} = \dfrac{5}{27}dt2d2P=275.
Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 327 questions covering 12.1 Gradients of Curves, 12.2 Differentiation from first principles, 12.3 Differentiating x^n, 12.4 Differentiating Quadratics, 12.5 Differentiating functions with two or more terms, 12.6 Gradients, Tangents and Normals, 12.7 Increasing and Decreasing Functions, 12.8 Second Order Derivatives, 12.9 Stationary Points, 12.10 Sketching Gradient Functions, and 12.11 Modelling with Differentiation, 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.
