The weekly number of tourists visiting an island is approximated by the equation given below y equals 30 plus 10 sine left bracket startfraction pi over 26 endfraction left parenthesis x minus 14 right parenthesis right bracket where y is the number of visitors (in thousands) in the xth week of the year, starting with x equals 1 for the first week in january. find the week in which the number of tourists to the island is

a. 40 comma 000 ,

b. 35 comma 000 , and

c. 25 comma 000

The first thing we must do for this case is to rewrite the function correctly:

"y equals 30 plus 10 sine left bracket startfraction pi over 26 endfraction left parenthesis x minus 14 right parenthesis right bracket"

Rewriting:

y = 30 + 10 * sine [pi / 26 * (x-14) ]

We substitute the value of y for each case and clear x.

We have then:

a. 40 comma 000:

40 = 30 + 10 * sine [pi / 26 * (x-14) ]

x = 27

b. 35 comma 000

35 = 30 + 10 * sine [pi / 26 * (x-14) ]

x = 18.33

c. 25 comma 000

25 = 30 + 10 * sine [pi / 26 * (x-14) ]

x = 9.66