select the correct answer.\nan earthquake registers a 5.6 on the richter scale. if the reference intensity…

select the correct answer.\nan earthquake registers a 5.6 on the richter scale. if the reference intensity of this quake was $7.3 \\times 10^{9}$, what was the intensity of the earthquake?\na. $2.70 \\times 10^{2}$\nb. $3.98 \\times 10^{5}$\nc. $1.30 \\times 10^{9}$\nd. $1.97 \\times 10^{12}$\ne. $2.91 \\times 10^{15}$

select the correct answer.\nan earthquake registers a 5.6 on the richter scale. if the reference intensity of this quake was $7.3 \\times 10^{9}$, what was the intensity of the earthquake?\na. $2.70 \\times 10^{2}$\nb. $3.98 \\times 10^{5}$\nc. $1.30 \\times 10^{9}$\nd. $1.97 \\times 10^{12}$\ne. $2.91 \\times 10^{15}$

Answer

Explanation:

Step1: Recall Richter scale formula

The Richter scale formula is $R = \log\left(\frac{I}{I_0}\right)$, where $R$ is the Richter magnitude, $I$ is the earthquake intensity, and $I_0$ is the reference intensity.

Step2: Rearrange to solve for $I$

Rearrange the formula to isolate $I$: $I = I_0 \times 10^R$

Step3: Substitute given values

Substitute $R=5.6$ and $I_0=7.3 \times 10^9$: $I = 7.3 \times 10^9 \times 10^{5.6}$

Step4: Calculate $10^{5.6}$

$10^{5.6} = 10^{5} \times 10^{0.6} \approx 100000 \times 3.981 = 3.981 \times 10^5$

Step5: Compute final intensity

$I \approx 7.3 \times 10^9 \times 3.981 \times 10^5 = (7.3 \times 3.981) \times 10^{9+5} \approx 29.06 \times 10^{14} = 2.91 \times 10^{15}$

Answer:

E. $2.91 \times 10^{15}$