Apps. and Interpretation for IBDP Maths Ebook 1 | Page 52

Your Practice Set – Applications and Interpretation for IBDP Mathematics
Exercise 13
1. A scientist defined the magnitude of an explosion by
N � 3log (2 E)
, N � 0.5
10
where N represents the magnitude of the explosion and E represents the amount of
energy released during the explosion.
(a)
(b)
Find the magnitude of an explosion if
the explosion.
3
5� 10 units of energy are released during
Find the amount of energy released during the explosion if the corresponding
magnitude of the explosion is 0.9.
[2]
[2]
2. A researcher defined the sound intensity level in an explosion by
Q�120 � 9.9log 10
I, I � 0
where
intensity.
Q dB represents the sound intensity level and
-2
I Wm represents the sound
If the sound intensity level increases from 139.8 dB to 169.5 dB, find the ratio of the new
sound intensity to the original sound intensity.
[5]
3. Consider the function f ( x) � 2x �3log 10( x � 2) , where x �� 2.
(a) Find the y -intercept of the function f( x ).
(b) Write down the number of x -intercept(s) of the function f( x ).
(c)
Solve the equation
f ( x)
2
� .
x
[2]
[1]
[3]
4. Consider the function f ( x) � x � log
10( x �10) � 2 , where x �� 10. The graph of f( x )
intersects the x -axis and the y -axis at A and B respectively. Let O be the origin. Find
the area of the triangle OAB.
[6]
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