An earthquake near New Zealand measured 4.2 on the Richter scale. Use the formula to determine approxima
how many times stronger the wave amplitude of the earthquake was than .

Ask by Davison Santiago. in the United States

Mar 29,2025

Question

An earthquake near New Zealand measured 4.2 on the Richter scale. Use the formula to determine approxima
how many times stronger the wave amplitude of the earthquake was than .

Ask by Davison Santiago. in the United States

Mar 29,2025

UpStudy AI · Accepted Answer

Given the Richter scale formula

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

we substitute $$ R = 4.2 $$ to obtain

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

To solve for $$\frac{A}{A_0}$$, we convert the logarithmic equation to its exponential form:

$$
\frac{A}{A_0} = 10^{4.2}.
$$

We can rewrite $$ 10^{4.2} $$ as

$$
10^{4.2} = 10^4 \times 10^{0.2} = 10000 \times 10^{0.2}.
$$

We approximate $$ 10^{0.2} $$. Since

$$
10^{0.2} \approx 1.585,
$$

we have

$$
\frac{A}{A_0} \approx 10000 \times 1.585 = 15850.
$$

Thus, the wave amplitude $$ A $$ is approximately $$ 15,849 A_0 $$, which matches the given answer choice.
The wave amplitude of the earthquake is approximately 15,849 times stronger than $$ A_{0} $$.

An earthquake near New Zealand measured 4.2 on the Richter scale. Use the formula to determine approxima
how many times stronger the wave amplitude of the earthquake was than .

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An earthquake near New Zealand measured 4.2 on the Richter scale. Use the formula to determine approxima how many times stronger the wave amplitude of the earthquake was than .

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An earthquake near New Zealand measured 4.2 on the Richter scale. Use the formula to determine approxima
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