Question

One formula for measuring the magnitude of an earthquake is by using the Richter scale. It is a logarithmic scale created by the following formula:
where M is the magnitude, Ic is the intensity of the movement of the earth from the earthquake in microns, and In is the intensity of the movement of the earth on a normal day to day basis in microns.
You can also write this magnitude out as where I is the intensity ratio of
The San Francisco earthquake of 1906 measured magnitude 8.3 on the Richter scale. Shortly afterward, an earthquake in South America had an intensity ratio four times greater than the San Francisco earthquake.
3ai) Write an equation in for the San Francisco earthquake.


aii) Re-write this equation as an exponential equation and solve it to find I.ø


aiii) Hence find the magnitude M on the Richter scale of the earthquake in South America.

b) A recent earthquake in Afghanistan measure 7.5 on the Richter scale. Find how many times more intense the San Francisco earthquake was.

c) Determine how much more intense is an earthquake who magnitude in 7.8 on the Richter scale than an earthquake who magnitude is 6.2

Answer 1

Answer:

Richter scale is a good way to talk about how strong an earthquake is. It is also easy to compare two earthquakes using the Richter scale.

Generally, earthquakes are estimated to be under

10

on the Richter scale.

Below is the formula for comparing two earthquakes.

M2-M1=log(I2-I1)

You can check out how this formula is derived.

Compute the magnitude of an earthquake

Given the intensity of two earthquakes and the magnitude of one of them, we can find the magnitude of the other earthquake. For example:

Earthquake

A

is

15

times stronger than earthquake

B

. Earthquake

B

is estimated to be

2.3

on the Richter scale. What is Earthquake

A

on the Richter scale?

M_A-M_B=log(I_A/I_B)

M_A-2.3=log(15)

M_A=log(15)+3.5

M_A=3.5

How much stronger is this earthquake comparing to that?

When given the magnitudes of

2

earthquakes, we can figure out how much stronger one earthquake is comparing to the other one. For example:

On the Richter scale, earthquake

A

is estimated to be

3

and earthquake

B

is estimated to be

1.5

.

How much stronger is earthquake

A

?

32

times

15

times

57

times

2

times

Step-by-step explanation:

The picture is the explanation......

And please comment if it helps you