The mass, m m\,m milligrams, of a culture of bacteria is modelled by
m=f(t)m = f(t)m=f(t), where f(t)=20e0.4tf(t) = 20e^{0.4t}f(t)=20e0.4t
and t t\,t is the time in hours after the culture is prepared, for 0≤t≤120 \leq t \leq 120≤t≤12.
Using set notation, state the range of fff. Give the upper limit to three significant figures.
Find an expression for f−1(m)f^{-1}(m)f−1(m), and state what f−1(m)f^{-1}(m)f−1(m) represents in this context.
Explain why this model should not be used to predict the mass of the culture three days after it is prepared.
566 exam-style questions on OCR A Level Maths 1.2 Algebra and Functions, covering 1.2.1 Indices, 1.2.2 Surds, 1.2.3 Simultaneous equations, 1.2.4 Quadratic functions, 1.2.5 Completing the square, 1.2.6 Solving quadratic equations, 1.2.7 Inequalities, 1.2.8 Expressing solutions of inequalities, 1.2.9 Representing inequalities graphically, 1.2.10 Manipulating polynomials, 1.2.11 Simplifying rational expressions, 1.2.12 The modulus function (A-level only), 1.2.13 Graphs of functions, 1.2.14 Sketching curves from equations, 1.2.15 Sketching reciprocal curves, 1.2.16 Interpreting solutions graphically, 1.2.17 Intersection points of graphs, 1.2.18 Proportional relationships, 1.2.19 Graph of the modulus of a linear function (A-level only), 1.2.20 Solving modulus equations graphically (A-level only), 1.2.21 Definition of a function (A-level only), 1.2.22 Inverse and composite functions (A-level only), 1.2.23 Simple graph transformations, 1.2.24 Combinations of graph transformations (A-level only), 1.2.25 Partial fractions (A-level only), and 1.2.26 Models in context. Each one has a worked solution and a mark scheme showing where the marks go.