Apps. and Interpretation for IBDP Maths Ebook 1 | Page 27

Exercise 5
1. The relationship between B , the boiling point of water in degrees Celsius, and x , the
vertical height above the sea level in metres, is given by B �100
�mx .
(a) Interpret what m represents.
It is given that the boiling point of water is 64 degrees Celsius at a height of 10 km.
[1]
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(b) Find the value of m .
[2]
(c) If water boils at the top of the Alphubel in Switzerland at 84 degrees Celsius, find
the height of the top of the Alphubel above the sea level.
[2]
2. The number of hotels in a city, N , can be modelled by N �at �b , where t is the
number of years after 2007.
(a) Interpret what b represents.
It is given that there are 143 hotels in 2007 and 193 hotels in 2012.
(b) Find the values of a and b .
(c) Find the number of hotels in 2015.
[1]
[3]
[2]
3. The daily salary of a worker is modelled by S �at �b , where $S is the salary of the
worker and t represents his working time in hours.
(a)
(b)
Interpret what a represents.
Interpret what b represents.
Stephen earns $600 after he has worked for 8 hours on a particular day, and the fixed
daily salary is $200.
(c) Find the values of a and b .
(d)
Find the daily salary if a worker only works for 30 minutes per day.
[1]
[1]
[3]
[2]
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