Question

1. a periodic function goes through 14 complete cycles in 8 minutes. what is the period of the function?

Explanation:

Step1: Recall the definition of period

The period of a periodic function is the time it takes to complete one full cycle. So we need to find the time per cycle.

Step2: Calculate the period

We know that in 8 minutes, there are 14 cycles. So the period \( T \) is the total time divided by the number of cycles. That is \( T=\frac{8}{14} \) minutes. Simplifying this fraction, we divide numerator and denominator by 2, getting \( T = \frac{4}{7}\approx0.571 \) minutes.

Answer:

The period of the function is \(\frac{4}{7}\) minutes (or approximately \( 0.57 \) minutes).