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1.8 Exponentials and Logarithms

1.8 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

1.8 Exponentials and Logarithms Questions

  1. A Level
  2. /Maths
  3. /1.8 Exponentials and Logarithms

104 exam-style questions on OCR (MEI) A Level Maths 1.8 Exponentials and Logarithms, covering 1.8.1 The function y = a^x, 1.8.2 Convert between index and logarithmic form, 1.8.3 Logarithm as inverse of exponential, 1.8.4 Laws of logarithms, 1.8.5 Values of log_a a and log_a 1, 1.8.6 Solve equations of the form a^x = b, 1.8.7 Reduce y = ax^n and y = ab^x to linear form, 1.8.8 The function y = e^x, 1.8.9 Gradient of e^kx (A-level only), 1.8.10 The function y = ln x, and 1.8.11 Exponential growth and decay. Each one has a worked solution and a mark scheme showing where the marks go.

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