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A warm can of soda is placed in a cold refrigerator. Sketch the graph of the temperature of the soda as a function of time. Is the initial rate of change of temperature greater or less than the rate of change after an hour?
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04:04
Daniel Jaimes
Calculus 1 / AB
Chapter 2
Limits and Derivatives
Section 7
Derivatives and Rates of Change
Limits
Derivatives
Missouri State University
Campbell University
University of Michigan - Ann Arbor
Lectures
04:40
In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.
In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.
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in this problem, a bomb can of soda is placed in a cold refrigerator, Right? So we need to sketch the graph of the temperature of soda as a function of time. And it is our secondly, that is the initial rate of change of temperature greater. All less than the rate of change after an earth. Right? So we need to scarce demographers. Then we need uh So let us let us now first discuss simply that if soda is yeah, soda has the room temperature, right? Or maybe it might be we are resuming that temperature is constant for the refrigerator for straight. So the temperature of the refrigerator is constant. But if we simply place any solder indeed, refrigerator, then obviously the initial rate of change of temperature will be greater than greater. Then the rate of change after another way. Because when it is placed after, when it is placed in a refrigerator, the temperature difference was more right? So the rate will be more uh rate of change will be rate of change of temperature will be more. Right? So, but after an hour, if it gets something colder, somewhat colder, then the temperature difference will be less. Right? So, initial rate of change of temperature should be greater. Then rate of things are eternal. So now let us write all the things now. So this is the graph we do lake, we will just discuss all the things. So when soda is placed in a fridge, the temperature starts to change quickly as the temperature of the refrigerator is very low as compared to soda late. So, as soon as the temperature of this order decreases the temperature difference between solder and depreciated. Also degrees Is is it? Yes. So now we will just sketch a graph this case, the graph of temperature of soda as a function of time. So this is the graph. Right? So this is our graph. And now secondly it is us. What the uh initial rate of change of temperature. Right? So we are just giving the reasons that why is it? So so as the difference of the temperature of soda and refrigerator also places the rate of change of temperature also decreases for this holder. Right? Does the rate of change of temperature of soda after an earth? Yes, less than the rate of change of temperature of soda before that are right. So that is why the initial rate of change of temperature is greater than the rate of change after. So, this is how we solve this problem. I hope you're an extremely concept. And here and here as the time passes, the temperature decreases. Right? So we are resuming like here somewhat The temperature was 72 and now it decreases to 38. Right? So we are assuming it. Right. So this isn't paranoid, we are just supposed to can write any other digits. But here we do in this way. So this red degrees is late, exponentially drained. So this is how we solve this problem. I hope you understand the concept. Thanks for watching
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