Question

A teacher hands out the following graph to four students who are asked to describe a real world situation that could be modeled by the graph. We may assume the graph runs from (0,10) to (9,0) and the graph is a curve and not a straight line. Chose the description below that least fits what is modeled by the graph

A) the weight of ten pounds of melting over time in a yard and taking nine hours to completely change into water and seep into the ground.

B) time in hours elapsed is on the x axis and temperature in degrees above room temperature is the y axis and the graph measures something cooling down over time

C) the volume of helium filled balloon that is slowly leaking air

D) the height of a rocket on the ground that first goes up and then comes down

Answer 1

A seems like best answer to me

Answer 2

We can definitely rule out (D) and (C) as a model with a negative concavity will be the perfect graph in order to model these events.

Now, let's look at (A) and (B) and compare these two.
(A) suggests that the melting ice takes nine hours to completely seep into the ground, and so, we can say that the y-axis represent the weight and this is a perfectly viable graph to do so.

(B) suggests that this graph can be used to represent temperature cooling down to room temperature. However, from temperature graphs, we know that temperature cools down faster when it's hotter moreso when it's around room temperature.

In order to understand this, we need to understand how turning a thermometer reacts with changes in the environment. When the difference between two temperatures is greater, the rate at which the thermometer is trying to pick up will react faster.

This essentially comes back to Newton's Law of Cooling, and so, this isn't the best suited graph to represent temperature changes.