Edexcel Mathematics Specimen paper · Paper 2 · Question 7 · ExamRizz

ExamRizzEdexcel MathematicsMathematics

Specimen paper · Paper 2 · Question 7 · 12 marks

7. A bacterial culture has area pmm^2 at time t hours after the culture was placed onto a circular dish. A scientist states that at time f hours, the rate of increase of the area of the culture can modelled as being proportional to the area of the cultu (a) Show that the scientist's model for p leads to the equation p= actr where a and k are constants. he scientist measures the values for pat regular intervals during the first 24 hours aft se culture was placed onto the dis le plots a graph of Inp against / and finds that the points on the graph lie close to aight line with gradient 0.14 and vertical intercept 3.' (b) Estimate, to 2 significant figures, the value of a and the value of k. (c) Hence show that the model for p can be rewritten as p= ab stating, to 3 significant figures, the value of the constant b. With reference to this model, (d) (i) interpret the value of the constant a, (ii) interpret the value of the constant b. (e) State a long term limitation of the model for p.

Lesson: Introduction to Differentiation and First Principles (Polynomials)