y is inversely proportional to x.
Find
percentage change in y when decreases by 50%
Since y is inversely proportional to x, we can write:
y = k/x
where k is a constant.
If x decreases by 50%, it becomes 0.5x. We can then find the new value of y using the same equation:
y' = k/(0.5x) = 2k/x
The percentage change in y is:
((y' - y)/y) * 100%
Substituting in the expressions for y and y':
((2k/x - k/x)/k/x) * 100%
Simplifying:
((k/x)/k/x) * 100%
= 100%
Therefore, the percentage change in y when x decreases by 50% is 100%.
To find the percentage change in y when it decreases by 50% in an inversely proportional relationship with x, we can use the formula for inverse proportionality:
y = k/x
where k is the constant of proportionality.
Let's assume the initial value of x is x₀ and the initial value of y is y₀. When y decreases by 50%, its new value becomes 0.5y₀. We need to find the new value of x, which we'll call x₁, that corresponds to this new value of y.
Using the formula for inverse proportionality, we can write:
y₁ = k/x₁
Since y₁ = 0.5y₀, we can substitute this into the equation:
0.5y₀ = k/x₁
Now, let's solve for x₁:
x₁ = k/(0.5y₀)
Since y is inversely proportional to x, we know that k = xy. Substituting this into the equation, we get:
x₁ = (xy)/(0.5y₀)
Simplifying further:
x₁ = 2xy/y₀
Now we can calculate the percentage change in y using the following formula:
percentage change = (new value - old value) / old value * 100%
percentage change = (0.5y₀ - y₀) / y₀ * 100%
Simplifying further:
percentage change = -0.5 * 100%
percentage change = -50%
Therefore, when y decreases by 50% in an inversely proportional relationship with x, there is a 50% decrease in y.