Question

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?

Answer 1

Explanation:

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

`BSA =(√(hm) )/(60)`

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 =
`BSA(80)-BSA(70)`

=
`(√(180*80) )/(60) -(√(180*70) )/(60) \\=2-1.871\\=0.129`

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

No BSA does not increase more rapidly