**
WELCOME TO THIS PAGE INTENDED FOR STUDENTS AT THE UNIVERSITY OF THE WESTERN CAPE
REGISTERED IN 2010 FOR THE MODULE:**

**
QSF 132**

SALARY NOTCHES

__QUESTION 1 (From QSF
June 2008 paper)__

In 2007 it was proposed by the South African
educational authorities that teachers’ salaries would range from R115 000
to R459 000 per annum. The salary range was divided into 74 notches, with
R115 000 being the 1^{st} notch and R459 000 being the 74^{th}
or last notch.

1.1 Express the ratio of R115 000 to R459 000 in its simplest form;

1.2 By what percentage is R459 000 ** more
than** R115 000? (Give your answer to the nearest
percentage.)

1.3 ** If
the difference between any two consecutive notches is a constant,
determine that constant
difference**.

1.4 Is the percentage increase from one notch
to the next consecutive notch also a constant? Motivate your answer by
calculating the percentage increase from the 1^{st} notch
to the 2^{nd} , and that from the second last to the last notch.
(7)

__
QUESTION 2__

In 2009 it determined by the South African
educational authorities that salaries would range from R62 418 to R542 271
per annum. The salary range was divided into 221 notches, with R62 418
being the 1^{st} notch and R542 271 being the 221^{st} or
last notch.

2.1 Express the ratio of R62 418 to R542 271 in
its **simplest form**;

2.2 By what
percentage is R542 271 *more than* R62 418? (Give your answer to the
nearest percentage

2.3 If the percentage increase from
one notch to the next is a * constant* of 1%,
calculate the second notch, the second last notch etc.

2.4 Do you agree that with the * assumption of a 1%*
increase from one notch to the

next?** **

2.5 Use the formula:

where *r =* 1.01,
in order to answer question 2.4 (if you have not done so already).

2.6 In 2010 it was agreed that all salary
notches would be adjusted by 7.5% * upwards*. Calculate the

2.7 In terms of the 2010 agreement, do the
salaries relevant to consecutive notches * still differ* by
the ratio of 1%?

__
QUESTION 3 __

Use the formula ,

together with the number of notches = 221, first term = R62 418 and last
term = R542 271, and prove by means of
*logarithms*
that *r =
* 1.01.

__
SOLUTION__:

If

then

**© DESMOND DESAI,
DMD EDU-HOME, 2010**

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