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.
717 exam-style questions on Edexcel A Level Maths Differentiation, covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change. Each one has a worked solution and a mark scheme showing where the marks go.