X is proportional to the square root of y where y >0 Y is increased by 44% Work out the percentage increase in x
There a few different ways of working this out. 1) x is proportional to the square root of y. So, if y doubles, x increases by 2. So an increase in y of 44% leads to an increase in x of 1.44=1.2, or 20%.
2) (A bit more formal) X is proportional to square root of y, so x=ky. Rearranging for the constant, k: k=yx. This constant is the same for all x and y. Let x1 and y1 be the original values and x2 and y2 be the new values, where y2=1.44y1.
y1x1=y2x2
The fraction x1x2 is the number of times bigger x2 is than x1.
x1x2=y1y2=y1y2=y11.44y1=1.44=1.2. Therefore a 20% increase.
3) You could pick actual numbers and see what happens.