The strength of earthquakes is measured on the Richter magnitude scale, with valuestypically between and where is the most severe.
The Gutenberg–Richter equation gives the average number of earthquakes per year, ,which have a magnitude of at least . For a particular region the equation is
, for some.
This region has an average of earthquakes per year with a magnitude of at least .
The equation for this region can also be written as.
The expected length of time, in years, between earthquakes with a magnitude of atleast is.
Within this region the most severe earthquake recorded had a magnitude of .
Find the value of .
(M1)
A1
[2 marks]
Find the value of .
EITHER
(M1)
OR
(M1)
THEN
A1
[2 marks]
Given , find the range for .
A1A1
Note: Award A1 for correct endpoints and A1for correct inequalities/interval notation.
[2 marks]