Question

In the sequence 5, 2, 10, 4, 15, 6, 20, 8, determine the constant of proportionality. State the result in pounds per minute.

a) 0.5 pounds per minute
b) 0.8 pounds per minute
c) 1.2 pounds per minute
d) 1.6 pounds per minute

Answer 1

The constant of proportionality in the given sequence is 2.5 pounds per minute, as each increase of 1 in the second number results in an increase of 5 in the first number.

Step-by-step explanation:

To determine the constant of proportionality in the sequence 5, 2, 10, 4, 15, 6, 20, 8, we must recognize the pattern of how numbers are related to each other. We can see that every second number is increasing by 2 (2, 4, 6, 8), and every first number before it is also increasing with each step (5, 10, 15, 20), which is 5 times the second number. Therefore, for each increase of 1 in the second number, the first number increases by 5.

Now, let's set up a ratio to represent this relationship. A constant of proportionality is the ratio of the two quantities that is always the same. In this case, if we take the first number (pounds) and divide it by the second number (minutes), we will get a constant ratio. Using the first pair as an example: 5 pounds / 2 minutes = 2.5 pounds per minute. This is the same for the subsequent pairs: 10 pounds / 4 minutes = 2.5 pounds per minute, and so on.