The population NNN of a specific bacteria culture, in thousands, is modeled by the equation
N(t)=(2t+2)28+122t+23 N(t) = \frac{(2t+2)^2}{8} + 12\sqrt[3]{2t+2} N(t)=8(2t+2)2+1232t+2for t≥0t \ge 0t≥0, where ttt is the time in hours since the start of an experiment.
Find an expression for dNdt\frac{dN}{dt}dtdN.
The point PPP with coordinates (3,32)(3, 32)(3,32) lies on the graph of the population model. Find an equation of the tangent to the curve at the point PPP.
Show that the model predicts no stationary points for the population for t≥0t \ge 0t≥0.
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.
