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1.6 Exponentials and Logarithms

1.6 Exponentials and Logarithms

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Question 59

A scientist is studying the growth of a synthetic crystal in a laboratory. The mass of the crystal, MMM grams, recorded ddd days after the growth process began, is modelled by the equation

log⁡10M=0.0607d+1.1760≤d≤20 \log_{10} M = 0.0607d + 1.176 \quad 0 \le d \le 20 log10​M=0.0607d+1.1760≤d≤20
a.

Show that this equation may be written in the form

M=abd M = ab^d M=abd

where aaa and bbb are constants to be found. Give the value of aaa to the nearest integer and give the value of bbb to 3 significant figures.

[3]
b.

Use the model to predict the mass of the crystal 20 days after the growth process began. Give your answer to 2 significant figures.

[2]
Markscheme

1.6 Exponentials and Logarithms Questions

  1. A Level
  2. /Maths
  3. /1.6 Exponentials and Logarithms

104 exam-style questions on OCR A Level Maths 1.6 Exponentials and Logarithms, covering 1.6.1 Properties of the exponential function, 1.6.2 Gradient of e^(kx) (A-level only), 1.6.3 Definition of the logarithm, 1.6.4 The natural logarithm function, 1.6.5 ln x as inverse of e^x, 1.6.6 Laws of logarithms, 1.6.7 Equations involving exponentials, 1.6.8 Reduction to linear form, and 1.6.9 Modelling using exponential functions. Each one has a worked solution and a mark scheme showing where the marks go.

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