Interpret model constants

A question is this type if and only if it requires giving a practical interpretation of constants in an exponential model in the context of the problem.

2 questions · Moderate -0.8

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Edexcel PMT Mocks Q12
9 marks Moderate -0.8
12. The table shows the average weekly pay of a footballer at a certain club on 1 August 1990 and 1 August 2010.
Year19902010
Average weekly pay\(\pounds 2500\)\(\pounds 50000\)
The average weekly pay of a footballer at this club can be modelled by the equation $$P = A k ^ { t }$$ where \(\pounds P\) is the average weekly pay \(t\) years after 1 August 1990, and \(A\) and \(k\) are constants.
a. i. Write down the value of \(A\).
ii. Show that the value of \(k\) is 1.16159 , correct to five decimal places.
b. With reference to the model, interpret
i. the value of the constant \(A\),
ii. the value of the constant \(k\), Using the model,
c. find the year in which, on 1 August, the average weekly pay of a footballer at this club will first exceed \(\pounds 100000\).
WJEC Unit 1 Specimen Q15
8 marks Moderate -0.8
15. The size \(N\) of the population of a small island at time \(t\) years may be modelled by \(N = A \mathrm { e } ^ { k t }\), where \(A\) and \(k\) are constants. It is known that \(N = 100\) when \(t = 2\) and that \(N = 160\) when \(t = 12\).
  1. Interpret the constant \(A\) in the context of the question.
  2. Show that \(k = 0 \cdot 047\), correct to three decimal places.
  3. Find the size of the population when \(t = 20\).