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.
532 exam-style questions on AQA A Level Maths 1.5 B: Algebra and functions, 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). Each one has a worked solution and a mark scheme showing where the marks go.