Q:

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 isa. 40 comma 000​,b. 35 comma 000​, andc. 25 comma 000

Accepted Solution

A:
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