Questions FD2 - A-Level Maths

8. The owner of a new company models the number of customers that the company will have at the end of each month. The owner assumes that

a constant proportion, \(p\) (where \(0 < p < 1\) ), of the previous month's customers will be retained for the next month
a constant number of new customers, \(k\), will be added each month.

Let \(u _ { n }\) (where \(n \geqslant 1\) ) represent the number of customers that the company will have at the end of \(n\) months. The company has 5000 customers at the end of the first month.

By setting up a first order recurrence relation for \(u _ { n + 1 }\) in terms of \(u _ { n }\), determine an expression for \(u _ { n }\) in terms of \(n , p\) and \(k\). The owner believes that \(95 \%\) of the previous month’s customers will be retained each month and that there will be 10000 new customers each month. According to the model, the company will first have at least 135000 customers by the end of the \(m\) th month.
Using logarithms, determine the value of \(m\). Please check the examination details below before entering your candidate information \section*{Further Mathematics} Advanced
PAPER 4D: Decision Mathematics 2 \section*{Answer Book} Do not return the question paper with the answer book.
1.
1 2 3 4
A 32 45 34 48
B 37 39 50 46
C 46 44 40 42
D 43 45 48 52
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2.
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3. 4. \begin{figure}[h]
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\end{figure} 5.
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6.
Stage State Action Destination Value
May 2 0 0 160
1 1 0 80 + 35
0 2 0 70

Stage State Action Destination Value

Month January February March April May
Number made
Minimum cost: \(\_\_\_\_\)
7. Player A \begin{table}[h]
\captionsetup{labelformat=empty} \caption{Player B}
Option W Option X Option Y Option Z
Option Q 4 3 -1 -2
Option R -3 5 -4 \(k\)
Option S -1 6 3 -3
\end{table} The tableau for (d)(ii) can be found at the bottom of page 16
b.v. □ □ □ □ Value
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8.

Questions FD2 (51 questions)

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Edexcel FD2 2022 June Q8

	Option W	Option X	Option Y	Option Z
Option Q	4	3	-1	-2
Option R	-3	5	-4	\(k\)
Option S	-1	6	3	-3

b.v.			□	□	□	□	Value
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