zachlebo 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
I do not know how to set up this problem and am confused by the exponents.
c
To solve this problem, we need to examine the information in the first sentence. We are told that “a reading of n + 1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of n.”
Let’s practice this idea with some real numbers. Let’s say n is 2. This means that n + 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: C
