Question

P = 100 - 20 cos (8πt/3) That's (8 pi t /3) where t is the time (in seconds). What is the period of the model? Discuss what the period represents in the context of this model.

Answer 1

Answer:

The period of the model is $\frac{3\pi}{4}$ seconds. The period represents the time needed for the function to complete one cycle.

Step-by-step explanation:

Cosine is a trigonometric function and trigonometric functions are characterized by having a periodical behavior. The period is the time needed for the function to cover an angle of $2\pi$ radians. By this approach we find that:

$\frac{8\pi\cdot t}{3} = \frac{2\pi\cdot t}{T}$ (1)

Where:

$t$ - Time, measured in seconds.

$T$ - Period, measured in seconds.

Then, we solve (1) for $T$:

$\frac{8}{3} = \frac{2\pi}{T}$

$T = \frac{6\pi}{8}\,s$

$T = \frac{3\pi}{4}\,s$

The period of the model is $\frac{3\pi}{4}$ seconds. The period represents the time needed for the function to complete one cycle.