It is given that y

Question

is directly proportional to x3.
Find the percentage increase in y when x increases by 100%

Answer 1

If y is directly proportional to x3, we can write:

y = kx3

where k is the constant of proportionality. To find the percentage increase in y when x increases by 100%, we need to find the new value of y when x is doubled (increased by 100%).

If x is doubled, the new value of x is 2x, so:

y' = k(2x)3

y' = 8kx3

The percentage increase in y is given by:

[(y' - y) / y] x 100%

Substituting the expressions for y and y' and simplifying, we get:

[(8kx3 - kx3) / kx3] x 100%

= 700%

Therefore, when x increases by 100%, y increases by 700%.