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1.6 Exponentials and Logarithms

1.6 Exponentials and Logarithms

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Question 49

The decay of a radioactive substance is modelled using the formula N=1000e−ktN = 1000e^{-kt}N=1000e−kt where N N\,N is the number of atoms after t t\,t years and k k\,k is a positive constant.

a.

Write down the number of atoms when the substance started to decay.

[1]
b.

Given that it takes 14.4 years for half of the substance to decay, find the value of k k\,k to 3 significant figures.

[4]
c.

Calculate the number of atoms left when t=30t = 30t=30.

[1]
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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