A scientist is modeling the growth rate VVV of a bacterial colony in terms of the concentration of a specific nutrient xxx. The relationship for x>0x > 0x>0 and x≠49x \neq 49x=49 is given by:
V=10.5+7x−1.5x12−x327−x V = \frac{10.5 + 7x - 1.5x^{\frac{1}{2}} - x^{\frac{3}{2}}}{7 - \sqrt{x}} V=7−x10.5+7x−1.5x21−x23Fully simplify the expression for VVV, justifying each step of your factorisation.
Practise AQA A Level Maths 1.5 B: Algebra and functions with exam-style questions for A Level Maths. 358 questions covering 1.5.1 Laws of indices, 1.5.2 Surds, 1.5.3 Quadratic functions, 1.5.4 Simultaneous equations, 1.5.5 Linear and quadratic inequalities, 1.5.6 Polynomials and rational expressions, 1.5.7 Graphs of functions and proportion, 1.5.8 Composite and inverse functions (A-level only), 1.5.9 Transformations of graphs, 1.5.10 Partial fractions (A-level only), and 1.5.11 Functions in modelling (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.
