Finding the Percentage Increase in y When x is Doubled

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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.
  • #1
topsyturvy
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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 :confused:

can somebody helpp to correct it??
thanks lotsa.:smile:
 
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  • #2
First, set up your general equation:
[tex]y=kx^{2}[/tex]
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:
[tex]y_{1}=kx_{1}^{2}[/tex]
and
[tex]y_{2}=kx_{2}^{2}[/tex]

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

Now, calculating [itex]y_{2}[/itex], we find:
[tex]y_{2}=kx_{2}^{2}=k(2x_{1})^{2}=4kx_{1}^{2}=4y_{1}[/tex]
Thus, calculating the percentwise increase, we have:
[tex]\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}[/tex]
Thus, if x increases with 100% , y increases with 300%.
 
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  • #3


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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