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 (x_{1},y_{1}),(x_{2},y_{2})[/tex] be two pairs of x and y values that satisfies your equation, that is: <br /> y_{1}=kx_{1}^{2}<br /> and<br /> y_{2}=kx_{2}^{2}<br /> <br /> Now, let x_{2}[/tex] represent a 100% increase of x_{1}, that is:&lt;br /&gt; x_{2}=2x_{1}[/tex]&amp;lt;br /&amp;gt; &amp;lt;br /&amp;gt; Now, calculating y_{2}, we find:&amp;lt;br /&amp;gt; y_{2}=kx_{2}^{2}=k(2x_{1})^{2}=4kx_{1}^{2}=4y_{1}&amp;lt;br /&amp;gt; Thus, calculating the percentwise increase, we have:&amp;lt;br /&amp;gt; \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}&amp;lt;br /&amp;gt; Thus, if x increases with 100% , y increases with 300%.