Question

"On the Richter scale, the magnitude R of an earthquake can be measured by the intensity formula

Answer 1

Answer:

  B)  The earthquake measuring 4.5 on the Richter scale is about 32 times more intense than an earthquake measuring 3.

Step-by-step explanation:

Let Ra = log(Ia/Io), and Rb = log(Ib/Io). Then for ...

  Ra - Rb = 4.5 -3.0 = 1.5

  log(Ia/Io) -log(Ib/Io) = 1.5 . . . . . . . . . . . substitute the given expressions

  (log(Ia) -log(Io)) -(log(Ib) -log(Io)) = 1.5 . . . expand the logs

  log(Ia) -log(Ib) = 1.5 . . . . simplify

  log(Ia/Ib) = 1.5 . . . . . . . . write as a single log

  Ia/Ib = 10^1.5 ≈ 32 . . . . take the antilog

The ratio of intensities is about 32, corresponding to choice B.