An earthquake is measured
with a wave amplitude
584 times as great as A sub zero.
What is the magnitude of
this earthquake using the
Richter scale to the nearest tenth.
For background information,
the Richter scale
is a logarithmic scale based
upon a logarithmic function.
The function is used to measure the
magnitude of earthquakes.
The magnitude of an earthquake
is related to how much
energy is released by the earthquake.
Instruments called seismographs
detect movement in the earth.
The smallest movement that can be detected
shows on a seismograph as a
wave with amplitude A sub zero.
So for the Richter scale
function or formula,
A equals the measure of the
amplitude of the earthquake wave
and A sub zero equals the amplitude
of the smallest detectable
wave called the standard wave.
From this, we can find R,
the Richter scale measurement
or magnitude of the earthquake
using the formula or log
function R equals log of A
divided by A sub zero.
Notice how there's no base
given on the logarithm,
which means this is common
log or log base ten.
Before going back to our question,
let's look at a table.
Because the Richter scale
is based upon the common log
or log base ten, every
level in the Richter scale
is ten times stronger
than the previous level.
Looking at the table below,
we have the Richter scale measurement
or magnitude on the far left,
then we have a description,
how often it occurs,
as well as the type of movement to expect.
And because each level is
ten times stronger than
the previous level,
if an earthquake has a
magnitude of let's say, five,
this would be ten times
stronger than an earthquake
with a magnitude of four.
So going back to our question,
we know we will be using
this equation or function
to determine the magnitude
of the earthquake.
And we're given the earthquake is measured
with a wave amplitude 584
times as great as A sub zero.
So because A
equals the measure of the
amplitude of the earthquake wave,
we know A must equal 584 times A sub zero.
So now using the Richter scale formula
R equals log of A divided by A sub zero,
we'll substitute 584 A sub zero for A
and then evaluate the log.
This will give us R, the
magnitude equals log of A
which is 584 A sub zero
divided by A sub zero.
Well A sub zero divided by
A sub zero is equal to one,
which means the magnitude of R is equal to
log of 584.
And now get out the calculator
to get a decimal approximation
for this logarithm.
The common log key is this button here,
so we press log,
enter 584,
close parentheses, enter.
We're asked to round to
the tenths place value
or one decimal place.
Because there's a six in
the hundredths place value,
we round up to approximately
two point eight.
So the magnitude of the earthquake
is approximately two point
eight on the Richter scale.
I hope you found this helpful.
