Finding the Percentage Increase in y When x is Doubled

[topsyturvy]

oic. thanks a lot.

y is directly proportional to x2
x is increased by 100%
find the percentage increase in y.

so,
y= k x2

then y= k x2
y=k 4 x2

so 4 x2 is already increased by 100%?
then to find k which is
y=k 4 x2
k= y/ 4 x2

find the percentage increase in y,
so what i did was :
y= y/4 x2 *100 x2

can somebody helpp to correct it??
thanks lotsa.

 

[arildno]

First, set up your general equation:
$$y=kx^{2}$$
Now, let [itex](x_{1},y_{1}),(x_{2},y_{2})[/tex] be two pairs of x and y values that satisfies your equation, that is:
$$y_{1}=kx_{1}^{2}$$
and
$$y_{2}=kx_{2}^{2}$$

Now, let [itex]x_{2}[/tex] represent a 100% increase of $x_{1}$, that is:
[itex]x_{2}=2x_{1}[/tex]

Now, calculating $y_{2}$, we find:
$$y_{2}=kx_{2}^{2}=k(2x_{1})^{2}=4kx_{1}^{2}=4y_{1}$$
Thus, calculating the percentwise increase, we have:
$$\frac{y_{2}-y_{1}}{y_{1}}*\frac{100}{100}=\frac{4y_{1}-y_{1}}{y_{1}}*\frac{100}{100}=3*\frac{100}{100}=\frac{300}{100}$$
Thus, if x increases with 100% , y increases with 300%.

 

[Architeuthis Dux]

Sure, I can help you correct your approach to finding the percentage increase in y. First, let's clarify the given information. The statement "y is directly proportional to x2" means that y is equal to some constant (k) multiplied by x2. So, we can write it as y = kx2.

Next, we are told that x is increased by 100%, which means it is doubled. So, if the original value of x is x1, after doubling it becomes 2x1.

Now, we want to find the percentage increase in y. To do this, we need to compare the new value of y (which we will call y2) to the original value of y (y1). Using the equation y = kx2, we can write y1 = kx1^2 and y2 = k(2x1)^2.

To find the percentage increase, we use the formula: (new value - original value)/original value * 100%. So, in this case, it would be (y2 - y1)/y1 * 100%.

Substituting in our values, we get ((k(2x1)^2 - kx1^2)/kx1^2) * 100%. Simplifying this, we get (3x1^2/kx1^2) * 100%. Since kx1^2 cancels out, we are left with 300%. This means that y has increased by 300% when x is doubled.

I hope this helps clarify the process for finding the percentage increase in y. Let me know if you have any other questions.