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1.3 Functions

1.3 Functions

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Question 126

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.

a.

Using set notation, state the range of fff. Give the upper limit to three significant figures.

[2]
b.

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.

[3]
c.

Explain why this model should not be used to predict the mass of the culture three days after it is prepared.

[1]
Markscheme

1.3 Functions Questions

  1. A Level
  2. /Maths
  3. /1.3 Functions

181 exam-style questions on OCR (MEI) A Level Maths 1.3 Functions, covering 1.3.1 Operations on polynomials, 1.3.2 Factor theorem, 1.3.3 Definition of a function (A-level only), 1.3.4 Composite functions (A-level only), 1.3.5 Inverse functions and their graphs (A-level only), 1.3.6 The modulus function (A-level only), 1.3.7 Inequalities with a modulus sign (A-level only), and 1.3.8 Functions in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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