Question

If the recommended adult dosage for a drug is $ D $ (in mg), then to determine the appropriate dosage $ c $ for a child of age $ a $ , pharmacists use the equation $ c = 0.0417D ( a + 1) $. Suppose the dosage for an adult is 200 mg. (a) Find the slope of the graph of $ c $. What does it represent? (b) What is the dosage for a newborn?

          If the recommended adult dosage for a drug is $ D $ (in mg), then to determine the appropriate dosage $ c $ for a child of age $ a $ , pharmacists use the equation $ c = 0.0417D ( a + 1) $. Suppose the dosage for an adult is 200 mg.

(a) Find the slope of the graph of $ c $. What does it represent?
(b) What is the dosage for a newborn?
        
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Added by Robert C.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
Chapter 1
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If the recommended adult dosage for a drug is $ D $ (in mg), then to determine the appropriate dosage $ c $ for a child of age $ a $ , pharmacists use the equation $ c = 0.0417D ( a + 1) $. Suppose the dosage for an adult is 200 mg. (a) Find the slope of the graph of $ c $. What does it represent? (b) What is the dosage for a newborn?
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Transcript

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00:01 Hi, today we are solving the question in which the equation for the appropriate dosage for a child of age a is given by c is equals to 0 .0417 d into a plus 1.
00:17 Now to find the slope of the graph of c, we need to rewrite the equation in slope -intercept form that is y is equals to m into x plus v where m is the slope, y is the dependent variable, x is the independent variable and b is the y -intercept.
00:35 So to do this we can substitute this as from above equation we can take it as c is equals to 0 .0417 d a plus 0 .0417 d.
00:53 Now we can see that the slope of the graph is 0 .0417 d which represent the rate of change here slope is m is equals to 0 .0417 d which represent the appropriate dosage of a child with respect to the age of child.
01:17 So we can say that therefore for every one unit increase in age of child the appropriate dosage increases by 0 .0417 d units.
02:00 Now taking the next one, so here we need to find the dosage for a newborn.
02:15 So we can substitute a is equals to 0 in the given equation.
02:20 So c is equals to 0 .0417 d into 0 plus 1.
02:27 So we get c as equals to 0 .0417 d...
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