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The quantity of oxygen that can dissolve in water depends on the temperature of the water. (So thermal pollution influences the oxygen content of water.) The graph shows how oxygen solubility $ S $ varies as a function of the water temperature $ T $. (a) What is the meaning of the derivative $ S'(T) $? What are its units?
(b) Estimate the value of $ S'(16) $ and interpret it.
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a) oxygen solubility ,per liter per degree Celsius.b. -0.25 milligrams
Calculus 1 / AB
Limits and Derivatives
Derivatives and Rates of Change
David Base G.
October 26, 2020
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October 27, 2020
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University of Nottingham
Idaho State University
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.
The quantity of oxygen tha…
Oxygen solubility The quan…
(a) Explain why the concen…
The graph shows the influe…
So in this problem were given the soluble bility of oxygen in water and it is a various with temperature we were given a graph T. In degrees C. And yeah, sigh ability? S in milligrams per leader. And we have a graph that looks something like this, right? Or this is 16 up here and on down. Okay. And the first question we're asked is, what does S prime at T. Was the meaning of the derivative. And what are its units? Well, this property means the rate at which the oxygen, sorry, ability yeah, changes with respect two temperature, specifically the temperature of water in this case. Okay. And the units will be milligrams for leader degrees C. Okay, then, the next thing we're asked to do is to estimate the value Value of s. prime at 16 and interpret it. All right part. So from the graph we can see that? S prime at 16. Yeah. Is s of 16 S. Of a. Yeah, over 16 minus eight. Which coming off the graph Is approximately 10 -12 over eight, which is going to be -2/8. Or negative 0.25. Okay. So what does that mean? That means is the temperature temperature past 16 degrees C. Yeah, the oxygen, sorry, ability is decreasing ah a rate 0.25 milligrams for leader degrees C.
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