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 AQA A Level Maths 1.10 G: Differentiation with exam-style questions for A Level Maths. 321 questions covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing 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.
