Which of the following terms increases and then decreases periodically as t increases?

A.)6cos(πt/26)
B.) πt/26

B) is a straight line with a slope of π/26.

that makes no since. if it's a straight line, wouldn't that mean it increases?

"if it's a straight line, wouldn't that mean it increases? "

Your second statement is correct. So which one is the correct answer, and why?

To determine which of the given terms increases and then decreases periodically as t increases, we need to analyze the behavior of the expressions.

Let's start with option A: 6cos(πt/26).

The cosine function oscillates (or repeats) periodically between -1 and 1 as its argument increases. In this case, the argument is πt/26. As t increases, the argument inside the cosine function increases, causing the cosine values to fluctuate between -1 and 1.

Since the term 6cos(πt/26) is multiplied by a positive constant (6), the entire expression will increase and decrease periodically as t increases.

Now let's consider option B: πt/26.

In this expression, the term πt/26 is a linear function of t. As t increases, the value of the term increases linearly. It does not exhibit any periodic behavior or fluctuations.

Therefore, the correct answer is A) 6cos(πt/26), as it increases and decreases periodically as t increases.