Question6) lab assistant sneaks into a grizzly bear's den during the winter months and hooks up a machine to monitor the bear's lung capacity in breathing. Luckily for the lab assistant, the bear is hibernating now. The lung capacity of the bear can be modelled by a sinusoidal function. a) Explain why the breathing of a hibernating grizzly bear can be modeled by a periodic function. b) Explain the meaning of the period in the context of this situation.
Studdy Solution
STEP 1
1. The bear's breathing is regular and repetitive during hibernation.
2. A sinusoidal function is a type of periodic function that can model repetitive phenomena.
STEP 2
1. Explain why the breathing can be modeled by a periodic function.
2. Explain the meaning of the period in this context.
STEP 3
The breathing of a hibernating grizzly bear can be modeled by a periodic function because it is a regular, repeating cycle. During hibernation, the bear's breathing pattern is consistent and follows a repetitive cycle, similar to the oscillation of a sine or cosine wave.
STEP 4
The period of a sinusoidal function represents the time it takes to complete one full cycle of the pattern. In the context of the bear's breathing, the period would be the duration of one complete breath cycle, from the start of an inhalation to the end of an exhalation and back to the start of the next inhalation.
The breathing of a hibernating grizzly bear is periodic due to its regularity, and the period represents the time for one complete breath cycle.
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