Chapter 1.

1.1 Problem Statement

8
rand(3,$a-1)
$a - $b
pow(10,$diff)

The Gutenberg-Richter Law states that the number, N, of earthquakes per year worldwide of Richter magnitude at least M satisfies an approximate relation log10(N) = a − M for some constant a. Find a, assuming that there is one earthquake of magnitude M ≥ 8 per year. How many earthquakes of magnitude M ≥ $b occur per year?

1.2 Step 1

In the logarithmic equation, log10(N) = a − M, we can solve for either M, N, or a when we are given values for two others.

We'll solve this equation first for a.

If there is one earthquake of magnitude 8 or greater per year, then, by substituting appropriately and simplifying, we get the following.

Question Sequence

Question 1.1

log10(N) = a − M

log10(0VV1JcqyBrI=) = a - nc1ItEz0kR4=

Incorrect
Correct

Question 1.2

Solve for a.

a = nc1ItEz0kR4=

Incorrect
Correct

1.3 Step 2

Question Sequence

Question 1.3

Substituting a = $a, the Gutenberg-Richter Law is log10(N) = $a − M.

For earthquakes of magnitude $b or greater, log10(N) = bPyFmFRwwelQ4hp0.

Incorrect
Correct

Question 1.4

To solve for N, we need the logarithm fact = pdlFLKGakEU= for any x ≥ 0 and any positive constant base b ≠ 1.

Incorrect
Correct

Question 1.5

In Step 3, we will apply this logarithm fact = Z83Mh9jMmzQ=.

Incorrect
Correct

1.4 Step 3

Thus, rewrite the equation, log10(N) = $diff, such that both sides become the exponent of 10. (Some authors refer to this as "exponentiating" both sides of the equation). We choose 10 for the base of the exponent since the given logarithm is base 10 and knowing that .

Question Sequence

Question 1.6

log10(N) = $diff

(Pz2PEfhsNWI=)$diff

Incorrect
Correct

Question 1.7

The expected number of earthquakes of magnitude $b or greater is as follows.

N = qjqZz1N+poo=

Incorrect
Correct