could be either, depending on the rate.
Increasing by 5 per day might be a lot worse than a 0.01% increase
Or, a 2% increase might get a lot worse than 25 per day.
For the first 30 days of a flu outbreak, the number of students on your campus who become ill is increasing. Which is worse: The number of students with the flu is increasing arithmetically or is increasing geometrically?
3 answers
Sounds like a sequence problem since the question is asking for arithmetic or geometric increases. There are formulas associated with these types of sequences but let's look at the BASIC textbook definitions:
In arithmetic sequences each term after the first differs from the one before it by a constant number. Also known as common difference. The common difference doesn't always have to be the same in the sequence but can vary. However, there is usually a pattern. For example, in the sequence:
2, 3, 5, 9, 17 we see that you add each term after 2 by 1, 2, 4, 8. So 2 + 1 = 3, 3 + 2 = 5, etc. However, in the sequence: 3, 5, 7, 9 you simply add each term after 3 by 2.
In geometric sequences each term after the first is multiplied by a non-zero constant number. Otherwise known as the common ratio.
For example: 1 , 2 , 4 , 8 , 16 each successive term is multiplied by 2 which is the common ratio. the common ratio(s): r = 2/1 = 2, r = 4/2 = 2, 8/4 = 2, etc.
In short, when something increases geometrically it grows exponentially and arithmetically usually means linearly. Diseases like the flu or meningitis in a high population environment like a college campus will most likely spread or geometrically. But you can make your own determination.
In arithmetic sequences each term after the first differs from the one before it by a constant number. Also known as common difference. The common difference doesn't always have to be the same in the sequence but can vary. However, there is usually a pattern. For example, in the sequence:
2, 3, 5, 9, 17 we see that you add each term after 2 by 1, 2, 4, 8. So 2 + 1 = 3, 3 + 2 = 5, etc. However, in the sequence: 3, 5, 7, 9 you simply add each term after 3 by 2.
In geometric sequences each term after the first is multiplied by a non-zero constant number. Otherwise known as the common ratio.
For example: 1 , 2 , 4 , 8 , 16 each successive term is multiplied by 2 which is the common ratio. the common ratio(s): r = 2/1 = 2, r = 4/2 = 2, 8/4 = 2, etc.
In short, when something increases geometrically it grows exponentially and arithmetically usually means linearly. Diseases like the flu or meningitis in a high population environment like a college campus will most likely spread or geometrically. But you can make your own determination.
In error, I told you the common difference varies. That is incorrect. Hence the word, common.
CORRECTION: The sequence
2, 3, 5, 9, 17 is neither geometric nor arithmetic even though we add each term after 2 by 1, 2, 4, 8. So 2 + 1 = 3, 3 + 2 = 5, etc. There is no common ratio either.
Sorry about that.
CORRECTION: The sequence
2, 3, 5, 9, 17 is neither geometric nor arithmetic even though we add each term after 2 by 1, 2, 4, 8. So 2 + 1 = 3, 3 + 2 = 5, etc. There is no common ratio either.
Sorry about that.