From the question info, we can deduce that :

y = k / √x , k is a constant.


When x = 100, y = 0.5,

0.5 = k / √100
0.5 = k / 10
k = 10(0.5)
k = 5


Now, 250% = 250/100 = 2.5

x is increased by 250% means x is increased by 2.5 times its original value. So it is now 3.5 times its original value.

Let y1 be the new value of y and x1 be the new value of x.

x1 = (1 + 2.5)x

= 3.5(100)
= 350


With x1 = 350, k = 5,

y1 = 5 / √350

y1 = 5 / √(25 x 14)

y1 = 5 / √25√14

y1 = 5 / 5√14

y1 = 1/√14

Or √14 / 14

Alternative :


Since x increases by 250% (2.5 times) , x is now 3.5 times its original.


As y is inversely proportional to the square root of x ,

y will now be 1/√3.5 times of the original value.

y = 0.5 x 1/√3.5

= 0.5/√3.5 x 2/2

= 1 / 2√3.5

= 1 / √(2² x 3.5)


= 1 / √14

or

√14 / 14


There is actually no need to fjnd k