The weekly number of tourists visiting an island is approxim

The weekly number of tourists visiting an island is approximated by the equation given below y= 20 + 10 sin[x/26(x - 11)] where y is the number of visitors (in thousands) in the x^th week of the year, starting with x = 1 for the first week In January Find the week in which the number of tourists to the island is 30,000, 25,000, and 15,000. The number of tourists to the island is 30,000 in week (Use a comma to separate answers as needed Round to the nearest integer as needed) The number of tourists to the island is 25,000 In week (Use a comma to separate answers as needed Round to the nearest integer as needed) The number of tourists to the island is 15,000 in week (Use a comma to separate answers as needed Round to the nearest integer as needed)

Solution

y=20 +10sin[pi/26(x-11)]    ( that have to be pi )

a. y= 30000

here y= 30000 and in the equation y represents the weekly number of tourists in thousand, therefore y=30

30=20 + 10sin[pi/26(x-11)]

(30-20)/10=sin[pi/26(x-11)]

26(sin ^-1(30-20)/10)=pi(x-11)

26*90/pi=x-11

13+11=x

x=24

b. y=25000

So we have to take y=25

And on setting it to the similar manner we get

26(sin^-1((25-20)/10))= pi(x-11)

780/pi=x-11

x=15.33

x=15(approximately)