Exponential & Logarithm Functions
Early in the century the earthquake in San Francisco registered 8.5 on the Richter scale. In the same year, another earthquake was recorded in South America that was four times more intense. What was the magnitude of the earthquake in South America, rounded to the nearest one decimal place?
1 Answer
Let $M_{SF}$ and $M_{SA}$ be magnitude of the earthquake in San Francisco and South America, respectively. Then
\[M_{SA}=\log\frac{I_{SA}}{S}=\log\frac{4 I_{SF}}{S}=\log 4+\log\frac{I_{SF}}{S}\]
\[=\log 4+8.5=0.602+8.5\approx9.1\]
Thus
\[M_{SA} =9.1 \text{Richter scale}.\]
\[M_{SA}=\log\frac{I_{SA}}{S}=\log\frac{4 I_{SF}}{S}=\log 4+\log\frac{I_{SF}}{S}\]
\[=\log 4+8.5=0.602+8.5\approx9.1\]
Thus
\[M_{SA} =9.1 \text{Richter scale}.\]
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