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The magnitude of an earthquake can be modeled by the formula R=log(II0)
, where I0=1
, What is the magnitude of an earthquake that is 3×104
times as intense as a zero-level earthquake? Round your answer to the nearest hundredth.



Answer :

To find the magnitude of the earthquake, we plug in the given intensity ratio into the formula:

R = log(I/I0)

Given that I = 3 × 10^4 times the intensity of a zero-level earthquake, we have:

I = 3 × 10^4 * I0

So, I = 3 × 10^4 * 1 = 3 × 10^4

Now, plug this into the formula:

R = log(3 × 10^4 / 1)

R = log(3 × 10^4)

Using the properties of logarithms, we can simplify this:

R = log(3) + log(10^4)

Since log(10^4) = 4, we have:

R = log(3) + 4

Now, calculate the logarithm of 3:

R ≈ 0.477 + 4

R ≈ 4.477

So, the magnitude of the earthquake is approximately 4.48 when rounded to the nearest hundredth.

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