Since we know that y is directly proportional to x^3, we can write:
y = kx^3
where k is a constant of proportionality.
Now, let's consider what happens when x decreases by 50%. This means that the new value of x, call it x', is equal to:
x' = 0.5x
To find the corresponding value of y', we substitute x' into our equation for y:
y' = k(x')^3
y' = k(0.5x)^3
y' = 0.125kx^3
So, the new value of y is 0.125 times the original value of y. This represents a decrease of 87.5% in y.
However, we are asked for the percentage increase in y. To find this, we need to use the formula:
% increase = (new value - old value) / old value x 100
Plugging in the values we found, we get:
% increase = ((0.125y - y) / y) x 100
% increase = (-0.875) x 100
% increase = -87.5
So, the percentage increase in y when x decreases by 50% is -87.5%, which represents a decrease in y.
It is given that y is directly proportional to x^3. Find the percentage increase in y when x decreases by 50%
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1 answer