In a resort town, the number of people employed during any given month, f (x) in thousands, can be modeled by function f (x) = 2.3 sin 30 (x+1) + 5.5, where x represents the month, with january = 1 and february = 2 and so one.

a. Approximately how many people are employed in August?

b. During which month is employed at it's highest level?

Question

Desmond Perry

Mathematics

24 July, 15:36

In a resort town, the number of people employed during any given month, f (x) in thousands, can be modeled by function f (x) = 2.3 sin 30 (x+1) + 5.5, where x represents the month, with january = 1 and february = 2 and so one.

a. Approximately how many people are employed in August?

b. During which month is employed at it's highest level?

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Answers (1)

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Sandra Avery · Answer 1

A. f (8) = (2.3sin (30) (8+1) + 5.5) (1000)

f (8) = (2.3 (.5) (9) + 5.5) (1000)

f (8) = (15.85) (1000)

f (8) = 15,850 people employed

b. f' (x) = 2.3sin (30) (1); on interval [1,12]

Because f' (x) turns out to be a positive number, the graph of f (x) just keeps increasing. Just plug in the highest number of the interval into the f (x) equation to get the highest number.

f (12) = (2.3 (.5) (12+1) + 5.5) (1000)

f (12) = (20.45) (1000)

f (12) = 20,450 people employed

The month with the highest number of people employed that year was December with a total of 20,450 people employed.