Apps. and Interpretation for IBDP Maths Ebook 1 | Page 51

13
Paper 1 – Logarithmic Models
Example
The magnitude of an earthquake can be modelled by the following function
M
�0.5 � log 10
P, P � 1
where M represents the magnitude of the earthquake and P represents the relative
energy released.
5
(a)
(b)
Find the magnitude of an earthquake if 2300 units of relative energy are released
in the earthquake.
[2]
Find the amount of relative energy released in an earthquake if the corresponding
magnitude of the earthquake is 5.1.
[2]
Solution
(a)
The required magnitude
�0.5 � log10
2300
(M1) for correct formula
� 3.861727836
� 3.86
A1 N2
(b) 5.1 �0.5 � log10
P
(M1) for substitution
4.6 � log10
P
log10
P �4.6 � 0
By considering the graph of y�log10
P� 4.6 ,
P � 39810.71706 .
Thus, the amount of relative energy is 39800 units. A1
N2
[2]
[2]
www.seprodstore.com
41