On a scale that measures the intensity of a certain phenomenon, a reading of n+1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of n. On that scale, the intensity corresponding to a reading of 8 is how many times as great as the intensity corresponding to a reading of 3?
a)5 b)50 c)10^5 d)5^10 e)8^10 - 3^10
A reading of n+1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of n.
Put another way:
Every time we move up one position in the scale, the intensity is multiplied by a FACTOR OF 10.
Thus:
A reading of 2 is 10 times a reading of 1.
A reading of 3 is 10 times a reading of 2.
A reading of 4 is 10 times a reading of 3.
A reading of 8 is how many times...a reading of 3?
Let a reading of 3 = 1.
Since every subsequent reading increases by a factor of 10, we get:
Reading of 4 = 10*1 = 10.
Reading of 5 = 10*10 = 100.
Reading of 6 = 10*100 = 1000.
Reading of 7 = 10*1000 = 10,000.
Reading of 8 = 10*10,000 = 100,000.
Since a reading of 8 = 100,000 and a reading of 3 = 1, a reading of 8 is 100,000 times a reading of 3.
The correct answer is
C.
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