Question

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?

O 5
O 50
O 10⁵
O 5¹⁰
O 8-3¹⁰

Answer 1

The intensity corresponding to a reading of 8 is 100,000 times as great as the intensity corresponding to a reading of 3, based on a scale where each unit increase represents a tenfold increase in intensity and is calculated as 10 to the power of the difference between readings, in this case, 10^5.

The correct option is option c.

Step-by-step explanation:

The student's question pertains to the concept of orders of magnitude in relation to intensity measurements on a certain scale. Specifically, we are asked how many times greater the intensity corresponding to a reading of 8 is compared to the intensity corresponding to a reading of 3, given that an increase of one unit (n + 1) on this scale indicates an intensity ten times that of n (10n).

To determine the difference in intensity between a reading of 8 and a reading of 3 on this scale, we calculate 10 to the power of the difference between these two readings (8 - 3), which is 105. Therefore, the intensity corresponding to a reading of 8 is 10 to the 5th power, or 100,000 times as great as the intensity corresponding to a reading of 3.