A woman has been yo-yo dieting for years. Her weight changes...

A woman has been yo-yo dieting for years. Her weight changes throughout the year as she gains and loses weight. Her weight in a particular month can be determined by the formula $w(x)=145+10 \cos \left(\frac{\pi}{6} x\right)$, where $x$ is the month and $w$ is in pounds. If $x=1$ corresponds to January, how much does she weigh in June?

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Key Concepts

Function Evaluation

Function evaluation is the process of substituting specific input values into a function to compute the corresponding output. This fundamental concept is applied when determining the value of a modeled quantity at a particular point in time.

Amplitude and Vertical Shift

Amplitude refers to the extent of variation in the oscillation of the function and indicates how far the values deviate from the central axis. The vertical shift represents the baseline or average value around which the oscillation occurs, providing context to the overall level of the measured quantity.

Trigonometric Functions

Trigonometric functions, such as the cosine function used in the model, are essential for describing oscillatory behavior. They are primarily involved in representing periodic phenomena, where the function's values repeat at regular intervals.

Periodic Functions

Periodic functions are those whose values repeat at fixed intervals, known as the period. They are critical in modeling processes that exhibit regular cyclical patterns, such as seasonal variations or repeated fluctuations in data.

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