Given a bottle with a height vs. volume graph that is created as the bottle is consistently filled with liquid, describe the correlation between the width of the bottle and the steepness of the graph?

The steepness of the graph will decrease when the width of the bottle is increased.

Step-by-step explanation:

We are told that a bottle with a height vs. volume graph is created asthe bottle is consistently filled with liquid

Now, from initial conditions, the bottle will be empty and immediately we start putting liquid into the bottle, the graph of height vs volume starts.

Now, this height(H) represents the height of the liquid in the bottle while volume(V) is the volume of liquid in the bottle.

Now, we want to find the correlation between the width of the bottle and the steepness of the graph.

Thus, if we are to increase the width of the bottle, it means we are also increasing the capacity of the bottle which is the volume of the bottle.

What this means is that for us to get to the same height(H) before the increase in bottle width, we will need to pour in a larger volume of liquid(V').

If the extra amount of liquid to be poured is v, then the new volume that will get the liquid to the initial height(H) is;

V' = V_initial + v

The implication of this is that the slope of the graph will decrease.

Thus in terms of the question, the steepness of the graph will decrease when the width of the bottle is increased.

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