On a scale that measures the intensity of a certain phenomenon, a reading of j+1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of j. 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? Choose the correct choice from the following choices.
A) 5 B) 50 C) 10^5 D) 5^10 E) 8^10 - 3^10
To solve this problem we need to examine the information in the first sentence. We are told that “a reading of j + 1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of j.”   Let’s practice this idea with some real numbers. Let’s say j is 2. This means that j + 1 = 3. With the information we were given we can say that a reading of 3 is ten times as great as the intensity of a reading of 2.   Furthermore, we can say that a reading of 4 is actually 10 x 10 = 10^2 times as great as the intensity of a reading of 2.   Increasing one more unit, we can say that a reading of 5 is 10 x 10 x 10 = 10^3 times as great as the intensity of a reading of 2.   We have found a pattern, which can be applied to the problem presented in the stem:   3 is “one” unit away from 2, and thus a reading of 3 is 10^1 times as great as the intensity of a reading of 2.   4 is “two” units away from 2, and thus a reading of 4 is 10^2 times as great as the intensity of a reading of 2.   5 is “three” units away from 2, and thus a reading of 5 is 10^3 times as great as the intensity of a measure of 2.   We can use this pattern to easily answer the question. Here we are being asked for the number of times the intensity corresponding to a reading of 8 is as great as the intensity corresponding to a reading of 3. Because 8 is 5 units greater than 3, a reading of 8 is 10^5 times as great as the intensity corresponding to a reading of 3.   Answer 10^5.
<result>C</result>
On a scale that measures the intensity of a certain phenomenon, a reading of j+1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of j. 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?