Question

W= 3.1 + l/2

The weight, w, in ounces, of a glass soda bottle design with a side length of l inches is given by the equation. By how many ounces does the weight of the bottle increase for every inch of increase in the side length?

Choose 1 answer:
A) 0.5
B) 2
C) 3.1
D) 3.6

Answer 1

A) 0.5

Explanation:

To find how much the weight of the bottle increases for every inch of increase in the side length, we need to find the derivative of the weight
`\sf w` with respect to the side length
`\sf l`.

Given the weight equation:

`\sf w = 3.1 + (l)/(2)`

Let's differentiate
`\sf w` with respect to
`\sf l`:

`\sf (dw)/(dl) = (1)/(2)`

This derivative tells us that for every one-inch increase in the side length
`\sf l`, the weight
`\sf w` increases by
`\sf (1)/(2) = 0.5` ounces.

Therefore, the answer is A) 0.5