Model with logarithmic relationship: find constant or predict value

Real-world context where the relationship is directly given in logarithmic form; requires finding an unknown constant or predicting a value using the given logarithmic model.

1 questions · Moderate -0.3

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Edexcel P2 2022 October Q4
8 marks Moderate -0.3
  1. The weight of a baby mammal is monitored over a 16 -month period.
The weight of the mammal, \(w \mathrm {~kg}\), is given by $$w = \log _ { a } ( t + 5 ) - \log _ { a } 4 \quad 2 \leqslant t \leqslant 18$$ where \(t\) is the age of the mammal in months and \(a\) is a constant.
Given that the weight of the mammal was 10 kg when \(t = 3\)
  1. show that \(a = 1.072\) correct to 3 decimal places. Using \(a = 1.072\)
  2. find an equation for \(t\) in terms of \(w\)
  3. find the value of \(t\) when \(w = 15\), giving your answer to 3 significant figures.