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Calculus/related rates

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Expert: - 3/14/2011


Question
Certain Chemotherapy dosages depend on a patient's surface ares. According to Mosteller model S= sqr root(hw)/60 where h is the patient's hight in centimeters, w is the patient's weight in Kg and S is the approximation of the patient's surface area in square meters. Assume that Tom's height is a constant 165 cm, but he is on a diet. If he loses 2kg/month, how fast is his surface area decreasing at the instant he weighs 70kg? Please clearly show all of your work and identify any numerical values you are subbing in for variables. Include units and round to 4 decimal places. I suck at related rates so i really need help on this one.

Answer
His surface area at 165cm and 70kg is approximated by S = sqrt(hw)/60.
Let's assume that Tom is full grown and the height is constant, so the only variable is w.

To find the rate of change of surface area with respect to time, assuming weight is a function of time as well, let's write the equation to signify this.  That is, S(t) = sqrt(hw(t))/60.

To take the derivative with respect to t gives S'(t) = (h/[60*sqrt(hw(t)])(w'(t)).
Since h, w(t), and w'(t) are known to be 165 cm, 70 kg, and -2 kg/month, respectively,
S'(t) can be found by substituting them  in.

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