an earthquake near new zealand measured 4.2 on the richter scale. use the formula r = log(a/a0) to determine…

an earthquake near new zealand measured 4.2 on the richter scale. use the formula r = log(a/a0) to determine approximately how many times stronger the wave amplitude of the earthquake was than a0. a = 0.62a0 a = 66,566a0 a = 15,849a0 a = 66.7a0

an earthquake near new zealand measured 4.2 on the richter scale. use the formula r = log(a/a0) to determine approximately how many times stronger the wave amplitude of the earthquake was than a0. a = 0.62a0 a = 66,566a0 a = 15,849a0 a = 66.7a0

Answer

Explanation:

Step1: Given the Richter - scale formula

$R=\log\left(\frac{A}{A_0}\right)$, and $R = 4.2$.

Step2: Rewrite the formula in exponential form

Since $R=\log\left(\frac{A}{A_0}\right)$ is equivalent to $10^R=\frac{A}{A_0}$ in exponential form.

Step3: Substitute the value of $R$

Substitute $R = 4.2$ into $10^R=\frac{A}{A_0}$. So, $\frac{A}{A_0}=10^{4.2}$.

Step4: Calculate $10^{4.2}$

$10^{4.2}\approx15848.93\approx15849$. So, $A = 15849A_0$.

Answer:

A. $A = 15,849A_0$