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Exponentials and Logarithms

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Question 62

Two experiments measuring the population of insects are started at the same time. PA=aeln⁡38t\displaystyle P_A = ae^{\frac{\ln 3}{8}t}PA​=ae8ln3​t and PB=beln⁡(5/2)8t\displaystyle P_B = be^{\frac{\ln(5/2)}{8}t}PB​=be8ln(5/2)​t. At the start (t=0t=0t=0) total is 244. After 8 days (t=8t=8t=8) total is 660.

a.

Show that a=100a = 100a=100, 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

Exponentials and Logarithms Questions

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

277 exam-style questions on Edexcel A Level Maths Exponentials and Logarithms, covering 14.1 Exponential Functions, 14.2 y = e^x, 14.3 Exponential Modelling, 14.4 Logarithms, 14.5 Laws of Logarithms, 14.6 Solving Equations using Logarithms, 14.7 Working with Natural Logarithms, and 14.8 Logarithms and Non-Linear Data. Each one has a worked solution and a mark scheme showing where the marks go.

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