Question

after a long period of seismic quiet, a sudden tremor hits a small town, registering a wave amplitude 280 times larger than ( a_0 ). what is the richter magnitude of this unexpected event, rounded to the nearest tenth? use the richter scale equation, r = logleft( \frac{a}{a_0}
ight) select one: (\bigcirc) a. 5.6 (\bigcirc) b. 144.5 (\bigcirc) c. 28 (\bigcirc) d. 2.4

Explanation:

Step1: Substitute given value

We know $\frac{A}{A_0}=280$, so substitute into the formula:
$R = \log(280)$

Step2: Calculate the logarithm

Use a calculator to find the value of $\log(280)$:
$\log(280) \approx 2.447$

Step3: Round to nearest tenth

Round 2.447 to one decimal place:
$2.447 \approx 2.4$

Answer:

D. 2.4