Carcass wrote:
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
STRATEGY: We could try to derive a formula that will help us calculate the intensity corresponding to a reading of 8.
However, it would be simple (and relatively fast) to use the "table method" to list each successive intensity reading.
This way, it will be easy to spot any mistakes we might make.Let
x the intensity corresponding to a reading of 3
So, our table, in the form
reading | intensity, will look like this:
3 | x4 | (x)(10)5 | (x)(10)(10)6 | (x)(10)(10)(10)7 | (x)(10)(10)(10)(10)8 | (x)(10)(10)(10)(10)(10)The intensity corresponding to a reading of 8 is how many times as great as the intensity corresponding to a reading of 3?Answer =
(x)(10)(10)(10)(10)(10) / x = (10)(10)(10)(10)(10)= 10⁵Answer: C