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The magnitude of an earthquake is given by the equation where I is the actual intensity of the earthquake and I₀ is the reference intensity (the smallest earth movement that can be recorded on a seismograph) .
-Find the intensity I of the earthquake given M(I) = 4.5. Round your answer to the nearest tenth.

Question

Use the following to answer questions :
The magnitude of an earthquake is given by the equation

where I is the actual intensity of the earthquake and I₀ is the reference intensity (the smallest earth movement that can be recorded on a seismograph) .
-Find the intensity I of the earthquake given M(I) = 4.5. Round your answer to the nearest tenth.

Quizplus · Accepted Answer

We need to solve the given equation M(I) = 4.5 for I. M(I) = log(I/I₀) / log(10) 4.5 = log(I/I₀) / log(10) log(I/I₀) = 4.5 * log(10) I/I₀ = 10^4.5 I = 10^4.5 * I₀ Using a calculator, we get: I ≈ 31,622.7766I₀ Rounding to the nearest tenth, we get: I ≈ 31,622.8I₀ Therefore, the best choice is B.

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