Math Snap

STEP 1

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

STEP 2

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

STEP 3

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

STEP 4

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

The problem asks for the intensity rounded to the nearest whole number. So, we round $$ to the nearest whole number.
$$\approx50119$$The intensity, $$, of an earthquake that has a magnitude of4.7 on the Richter scale is approximately50119.