# Finding the Percentage Increase in y When x is Doubled

• topsyturvy
In summary, the conversation discusses the relationship between x and y, specifically how y is directly proportional to x^2 and how a 100% increase in x results in a 300% increase in y. The conversation also provides an equation to calculate the percentage increase in y given specific x and y values.
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.

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

Last edited:

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.

## What is the formula for finding the percentage increase in y when x is doubled?

The formula for finding the percentage increase in y when x is doubled is (y2-y1)/y1 * 100%, where y1 represents the original value of y and y2 represents the new value of y after x is doubled.

## Can this formula be applied to any given situation?

Yes, this formula can be applied to any given situation where there is a change in y that is directly related to a doubling of x.

## How can this formula be used in real-world applications?

This formula can be used in various real-world applications, such as calculating the increase in sales when advertising budget is doubled, or determining the increase in production when the number of workers is doubled.

## What is the purpose of finding the percentage increase in y when x is doubled?

The purpose of finding the percentage increase in y when x is doubled is to understand the relationship between x and y and how changes in one variable can affect the other. It can also be used to make predictions and decisions based on the calculated increase.

## Is there a specific unit for the percentage increase in y when x is doubled?

No, the percentage increase in y when x is doubled is a unitless value, represented as a percentage. This allows for easy comparison between different situations or scenarios.

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