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The logarithmic function y = logx + 7.9 can be used to determine the magnitude, y, of an earthquake given an intensity comparison, x, of a previous earthquake—in this case, an earthquake with a rating of 7.9 on the Richter Scale. This function is graphed below.

What is the magnitude of an earthquake, y, that is 15 times as intense as the previous earthquake (rounded to the nearest tenth)? What intensity, x, is the aftershock, with a magnitude of y = 8.6 (rounded to the nearest whole number), compared with the original earthquake?

A. Magnitude of earthquake: y = 9.1, intensity comparison: x = 4 times 

B. Magnitude of earthquake: y = 8.9, intensity comparison: x = 3 times 

C. Magnitude of earthquake: y = 29.0, intensity comparison: x = 1 time 

D. Magnitude of earthquake: y = 9.1, intensity comparison: x = 5 times

 Jun 30, 2016
 #1
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We have, for the first question :

 

y = log (15) + 7.9  = 9.07  →  9.1

 

For the second, we have :

 

8.6 = lox x + 7.9        subtract 7.9 from each side

 

8.6 - 7.9  = log x

 

0.7 = log x    this says that x  =    100.7  ≈   about 5 times

 

The correct answer is  D

 

 

 

cool cool cool

 Jun 30, 2016

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