QuestionQuestion 5 (1 point) The function below is a model that describes the cyclical variation of the price of a stock share as a function of time in months from January 2023 ( $t=0$ corresponds to January). $P(t)=1.5 \cos \left(\frac{\pi}{4} t\right)+3.5$
What is the highest price per share? $\square$ A
What is the lowest price per share? $\square$ A In what month is the price lowest? (Type the month, starting with a capital.) $\square$ A

Studdy Solution
To find the month when the price is lowest, we need to determine when $\cos \left(\frac{\pi}{4} t\right) = -1$ .
The cosine function equals -1 at $\frac{\pi}{4} t = \pi + 2k\pi$ for integer $k$ . Solving for $t$ :
$\frac{\pi}{4} t = \pi$ $t = 4$
This corresponds to 4 months after January 2023, which is May 2023.
The month when the price is lowest is $\boxed{\text{May}}$ .

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