Earthquake intensity on the richter scale, the magnitude r of an earthquake of intensity i is given by
r = (ln i - ln i0)/ln 1o
where 10 is the minimum intensity used for comparison. assume 10 = 1.
(a) find the intensity of the march 11, 2011 earthquake in japan for which r = 9.0.
(b) find the intensity of the january 12. 2010 earthquake in haiti for which r = 7.0.
(c) fiind the factor by which the intensity is increased when the value of r is doubled.
(d) find dr/dl.

(A) 999 734 198.4

B) 9999043.54

C) the intensity L is squared when R is doubled

D) dR/dL = 1/(Lln10)

Step-by-step explanation:

R = (In L - ln Lo)/ ln 10

Since Lo = 1 and ln 1 = 0

Therefore,

R = ln L / ln 10

(A) Since R = 9

In L = Rln10

In L = 9 ln10 = 20.723

L = exp(20.723) = 999 734 198.4

Therefore, the intensity of earthquake in Japan = 999 734 198.4

(B) when R = 7

In L = Rln10

In L = 7ln10 = 16.118

L = exp(16.118) = 9999043.54

Therefore the intensity of earthquake in Haiti = 9999043.54

(C) when R is doubled, let say R = 14

L= exp(14ln10) = 99980871640000

Then the ratio of L(R=14) and L(R=7)

L(R=14)/L(R=7) = 99980871640000/9999043.54 = 9999043.53

Since L(R=14)/L(R=7) = L(R=7)

Therefore, the intensity L is squared when R is doubled

D) R = lnL/ln10

dR/dL = 1/(Lln10)