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Mathematics: AI HL

Paper 2

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Mathematics: AI HL

Available time 20 Minute(s)

Human Resource department has a piecewise function, T

Paper 2

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Available time 20 Minute(s)

01. Question

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Maximum Mark 8

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Human Resource department has a piecewise function, T to calculate the amount of bonus to be paid to employees, according to their annual performance rating, x given by

$T (x) = \{\begin{cases} 0 & x \leq 6 \\ \frac{(50 x - 2500)^{2}}{525} & 6 < x \leq 8 \\ 4 x + 10000 & 8 < x \end{cases}$

(a). Find the annual bonus to be paid by employees with annual performance rating of
(i) 7

[Marks: 1]

(ii) 9

[Marks: 1]

The management is considering increasing the bonus for next year and is contemplating the following two options:

Option 1 : Increase bonus by $1000 on all levels, and then by a factor of 0.8
Option 2 : Increase bonus using the model $T (4 x + 200)$

(b). Determine functions to model the bonus for each of these options, and calculate which option will pay higher bonus for a rating of 7.

[Marks: 6]

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