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1.6 Exponentials and Logarithms

1.6 Exponentials and Logarithms

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Question 24

Two experiments measuring the population of insects are started at the same time. PA=ae0.2tP_A = ae^{0.2t}PA​=ae0.2t and PB=be0.15tP_B = be^{0.15t}PB​=be0.15t. At the start (t=0t=0t=0) total is 120. After 8 days (t=8t=8t=8) total is 480.

a.

Show that a=50a = 50a=50, to the nearest whole number, and find the value of bbb.

[3]
b.

Estimate the total number of insects after 10 days.

[1]
c.

Find the day that the number of insects in experiment A exceed the number of insects in experiment B.

[3]
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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