Help me pls...?

Question

y is directly proportional to x^2.
x is increased by 100%.
Find the percentage increase in y.

The ans is 400%

Please show me your workings and explain cos I don't understand..thanks!

Answer 1

x increased by 100% is 2x
(2x)² = 2²x²=4x²
⇒ y has increase 4 times
⇒ y increased 400%

Answer 2

The fact that y is directly proportional to x^2 means that y is equal to x^2 times some constant multiple (I'll use the letter A to symbolize that constant multiple) so,

yo = old y
yn = new y (after the increase in x)

yo = Ax^2

if x is increased by 100%, that means it was doubled, so x = 2x

yn = A(2x)^2
yn = A4x^2

the percentage increase of yo is given by

(yn-yo)/yo * 100

or

(A4x^2-Ax^2)/(Ax^2) *100 = % increase

factoring the numberator to Ax^2(4-1), the Ax^2 canceles with the Ax^2 in the denominator leaving 3 *100 or 300%

It depends on the terminology, but y is increased by 300%.

The 400% would answer the question "What percentage of the initial y will the new y be?" or something like that. That would go as follows

yn/yo = yn percent of yo

A4x^2/Ax^2 * 100 = yn % of yo

again Ax^2 canceles leaving 4 * 100 or 400%

Answer 3

well, if y is proportional to x^2, y and x^2 will increase or decrease at the same rate.

So when x is increased by 100% it means (x+100%x) or (x+x) or (2x)

when this number is squared, it is equal to 4(x^2)

Now y is proportioanl to 1(x^2)... 4y is proportional to 4(x^2)

4y is equal to (400%) y

Answer 4

y / x^2 = k
so if x => 2x
y = k 4x^2

y is 4y which is increased by 400%