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Current time:0:00Total duration:3:22

Key features of graphs — Harder example

Video transcript

Ruby puts a dish of macaroni and cheese into the refrigerator the dish was eighty eighty degrees Fahrenheit when she put it in and the inside of the refrigerator was 40 degrees Fahrenheit the dish cooled quickly at first this is gonna be interesting quickly at first then slowed as it approached the temperature inside the refrigerator all right which of the following graphs in the m t plane could best represent the temperature T in degrees Fahrenheit M minutes after Ruby put the dish in the refrigerator so MT plane sounds very fancy but all they're saying is and the horizontal axis that's our time axis it's gonna be measured in minutes M for minutes and our vertical axis in this plane in this coordinate plane is going to be our temperature axis and it's measured in Fahrenheit degrees so let's see what what they're saying so the dish started at 80 at 80 degrees at 80 degrees Fahrenheit so it's zero minutes right when she put it into the fridge it should be 80 degrees so this one right over here this one is indeed at 80 degrees this graph right over here this is starting at zero degrees not it it should it needs to start at 80 degrees if we're gonna model what actually happened so this we can rule that one out immediately then when you look at these choices this one's starting at 40 degrees once again not what we need we need it to start at 80 degrees at zero minutes so overrule that one out this one also starts at 80 degrees now let's think about the shape of what the curve should be they say they say the dish cooled quickly at first then slowed then slowed as it approached the temperature inside the refrigerator now does this graph describe that it started before it was in the refrigerator at 80 degrees or right when they put in the refrigerator it's at 80 degrees and then it starts its temperature declines quickly at first but then the the the rate of decline slows as it approaches the temperature inside of frig that forty degrees and that seems like that this is what's happening it's B the slope is because it starts out quite negative but it becomes less and less and less negative as we get closer and closer to the forty degrees Fahrenheit this one over here after some number of minutes we do end up at this forty degrees Fahrenheit but the rate of decline is constant the entire time this is a line this is describing a constant rate of decline but what they described is a changing rate of decline the dish cooled quickly at first so that would be a steep declines cooled quickly at first then slowed as it approached the temperature inside the refrigerator so the decline slows it becomes less negative as we approach the temperature of the refrigerator so you have this this this this this change in the rate of a temperature change and so you are going to you or at least I would pick this one right over here this one right over here describes a constant rate which is not what was described in the question