The Richter scale is used to rate the magnitude of an earthquake by how much energy it releases. Below isa list of historic earthquakes, the energy released, and the rating on the Richter scale.EarthquakeNorthridge (USA), 1994Valdivia (Chile), 1960Tibet, 1950Mexico City, 1985Sumatra-Andaman, 2004y =Energy, measured in petajoules0.7112,202501892,818The rating on the Richter scale can be modelled by a logarithmic regression function of the formy a+b ln xwhere x is the energy of the quake, in petajoules (quadrillion Joules), and y is rating on the Richter scale.Determine a logarithmic regression function that could be used to model these data. Round the values of aand b to the nearest tenth.Richter scale6.79.58.68.19.1-In(x)According to the logarithmic regression function, determine the rating of an earthquake with 277petajoules of energy. Round to one decimal place.The rating ison the Richter scale.

The given Richter scale readings are, Earthquake Energy, measured in petajoules Richter scale North ridge (USA), 1994 0.7 6.7 Valdivia (Chile), 1960 112202 9.5 Tibet, 1950 501 8.6 Mexico city, 1985 89 8.1 Sumatra- Andaman, 2004 2818 9.1 We have to find the logarithm equation for this data.Let x is the energy of earthquake in petajoules and y is rating of the Richter scale. Logarithm regression can be calculated as, y=a+b lnx Where, a=y-b ln xb=SxySxxSxx=∑lnx-ln x2Sxy=∑lnx-ln xy-yCalculations: ln x=29.92045=5.9841y=425=8.4 x y ln x ln x-ln x y-y ln x-ln x2 ln x-ln xy-y 0.7 112202 501 89 2818 6.7 9.5 8.6 8.1 9.1 -0.3567 11.6281 6.2166 4.4886 7.9438 -6.3408 5.6440 0.2325 -1.4955 1.9597 -1.7 1.1 0.2 -0.3 0.7 40.2055 31.8547 0.0541 2.2365 3.8404 10.7794 6.2084 0.0465 0.4487 1.3718 42 29.9204 78.1912 18.8548 Now, b=18.854878.1912=0.2411a=8.4-18.854878.19125.9841=6.9570 The logarithm line becomes y=6.957+0.2411 lnx Rounding up to one decimal place, we get y=7.0+0.2 ln(x).The earthquake is 277 petajoules, Put x=277 in y=7.0+0.2 ln(x) y=7.0+0.2 ln277=7.0+1.1248=8.1248y≈8.1 The rating is 8.1 on the Richter scale.Final answer: The logarithm regression line is y=7.0+0.2 ln(x) The rating on the earthquake with 277 petajoules of energy is 8.1 on the Richter scale.