no numerical values are provided. Just a concept based understanding problem 2. For each of the scenarios below, construct a graph of the height of the water in the bottle as a functionof the volume of water in the bottle. Then, make an illustration of a bottle that would produce aheight-volume graph with that general shape.Scenario #1: A bottle in which the height of the water in the bottle increases at a constant ratewith respect to the volume of water in the bottle.b. Scenario #2: A bottle in which the height of the water in the bottle increases at a constant ratewith respect to the volume of water in the bottle, then increases at a decreasing rate with respectto the volume of water in the bottle.а.Scenario #3: A bottle in which the height of the water in the bottle increases at an increasing ratewith respect to the volume of water in the bottle, then increases at a constant rate with respect tothe volume of water in the bottle, then increases at a decreasing rate with respect to the volume ofwater in the bottle.с.

Name: no numerical values are provided. Just a concept based understanding p
Uploaded: 2024-03-20T07:07:37.000Z
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Description: no numerical values are provided. Just a concept based understanding problem 2. For each of the scenarios below, construct a graph of the height of the water in the bottle as a functionof the volume of water in the bottle. Then, make an illustration

Note: numerical values are not mentioned as per the question. For each scenario below, we will construct a graph of the height of the water in the bottle as a function of the volume of water in the bottle. For (a), Scenario #1: A bottle in which the height of the water in the bottle increases at a constant rate with respect to the volume of water in the bottle. We know that increases at a constant rate imply the graph will be a line with the increasing rate (slope>0). So, the graph looks like the following.For (b), Scenario #2: A bottle in which the height of the water in the bottle increases at a constant rate with respect to the volume of water in the bottle, then increases at a decreasing rate with respect to the volume of water in the bottle. The above implies that the beginning part of the graph increases at a constant rate that means the beginning part of the graph will be a line with the increasing rate (slope>0). Then the rest part of the graph increases at a decreasing rate. Note: If f is concave down at a point, the slopes are decreasing, and it looks as if it is tailing off. We can say "f is increasing at a decreasing rate." Thus, the graph looks like the following.For (c), Scenario #3: A bottle in which the height of the water in the bottle increases at an increasing rate with respect to the volume of the water in the bottle, then increasing at a constant rate with respect to the volume of water in the bottle, then increases at a decreasing rate with respect to the volume of water in the bottle. The above implies that the first part of the graph increases at an increasing rate. And we know that If f is concave up or convex at a point, the slopes are increasing, and it looks as if it is tailing off. We can say "f is increasing at an increasing rate." Further, the second part of the graph increasing at a constant rate that means the second part of the graph will be a line with the increasing rate (slope>0). And then the graph increases at a decreasing rate. And we know that If f is concave down at a point, the slopes are decreasing, and it looks as if it is tailing off. We can say "f is increasing at a decreasing rate." Thus, the graph satisfying the above properties looks like the following.