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QuestionFind the intensity II of an earthquake with a magnitude of 4.7 using R=log⁡(I1)R=\log \left(\frac{I}{1}\right). Round to the nearest whole number.

Studdy Solution

STEP 1

Assumptions1. The formula for the magnitude of an earthquake is R=log⁡(0)R=\log \left(\frac{}{_{0}}\right). 0=1_{0}=1
3. The magnitude of the earthquake, RR, is4.7

STEP 2

We are given the magnitude of the earthquake and we need to find the intensity, .Wecanrearrangetheformulatosolvefor. We can rearrange the formula to solve for .
=I0×10R = I_{0} \times10^{R}

STEP 3

Now, plug in the given values for 0_{0} and RR to calculate the intensity.
=1×10.7 =1 \times10^{.7}

STEP 4

Calculate the intensity, $$.
=1×104.7≈50118.72336272722 =1 \times10^{4.7} \approx50118.72336272722

STEP 5

The problem asks for the intensity rounded to the nearest whole number. So, we round $$ to the nearest whole number.
≈50119 \approx50119The intensity, $$, of an earthquake that has a magnitude of4.7 on the Richter scale is approximately50119.

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