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To determine drug dosages, doctors estimate a person’s body surface area (BSA) (in meters squared) using the formula BSA = √ h m / 60 , where h is the height in centimeters and m the mass in kilograms. Calculate the rate of change of BSA with respect to mass for a person of constant height h = 180 . What is this rate at m = 70 and m = 80 ? Express your result in the correct units. Does BSA increase more rapidly with respect to mass at lower or higher body mass?

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Answer:

Step-by-step explanation:

Given that a person’s body surface area (BSA) (in meters squared) using the formula

[tex]BSA =\frac{\sqrt{hm} }{60}[/tex]

We are to calculate the rate of change of BSA with respect to mass for a person of constant height h = 180 from m =70 to m =80

For this we calculate BSA for 80 kg and BSA for 70 kg first

Rate of change = [tex]BSA(80)-BSA(70)[/tex]

=[tex]\frac{\sqrt{180*80} }{60} -\frac{\sqrt{180*70} }{60} \\=2-1.871\\=0.129[/tex]

i.e. rate of change per 10 kg is 0.129

No BSA does not increase more rapidly

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