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Intensity Question

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by sanchu » Mon Feb 10, 2014 4:00 pm
On a scale that measure the intensity of a certain phenomonenon, a reading of n+1 corresponds to the intensity that is 10 times the intensity corresponding to a reading o 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
c)5^10
d) 8^10-3^10
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by Bill@VeritasPrep » Mon Feb 10, 2014 4:08 pm
sanchu wrote:On a scale that measure the intensity of a certain phenomonenon, a reading of n+1 corresponds to the intensity that is 10 times the intensity corresponding to a reading o 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
c)5^10
d) 8^10-3^10
I did a quick table of values:

reading of 1 = 1
reading of 2 = 10
reading of 3 = 10^2
reading of 4 = 10^3
reading of 5 = 10^4
reading of 6 = 10^5
reading of 7 = 10^6
reading of 8 = 10^7

The difference between the exponents is 5: 10^2 * 10^5 = 10^7. Go with C.
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by [email protected] » Tue Feb 11, 2014 12:32 am
Hi sanchu,

Bill has correctly explained the logic behind the prompt. I'm going to present the information in a slightly different way (using the vocabulary the prompt uses):

Let's say that the "first level" of a phenomenon is N.

So, the "second level" would be 10 times the "first level" = 10N
The "third level" would be 10 times the "second level" = 10(10N) = 100N
The "fourth level" would be 10 times the "third level" = 10(100N) = 1,000N
Etc.

The pattern is that each level is "10 times" greater than the prior level. With that pattern, a "reading of 8" relative to a "reading of 3" is a difference of 10(10)(10)(10)(10)N = (N)10^5

Final Answer: C

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