Question

PLEASE HELP ME

David and Ronald both are making cubic gift boxes with varying volume. The side length of David's gift box for a given volume is given by the function below, where (x - 1) is the volume of the box, in cubic feet.


The side length, g(x), of Ronald's gift box for a given volume is shown in the table below, where x is the volume of the box, in cubic feet.


Whose gift box has the greater side length for a given volume?

Answer 1

The answer would be Ronald. Also this is for plato too.

Explanation:

Answer 2

Option C Both gift boxes have the same length for a given volume

Explanation:

step 1

David's gift box

Calculate the side length of the box for a given volume

we have

`f(x)=\sqrt[3]{x-1}`

For
`(x-1)=2\ ft^(3)` ------>
`f(x)=\sqrt[3]{2}=1.26\ ft`

For
`(x-1)=4\ ft^(3)` ------>
`f(x)=\sqrt[3]{4}=1.59\ ft`

For
`(x-1)=6\ ft^(3)` ------>
`f(x)=\sqrt[3]{6}=1.82\ ft`

For
`(x-1)=10\ ft^(3)` ------>
`f(x)=\sqrt[3]{10}=2.15\ ft`

therefore

Both gift boxes have the same length for a given volume