Answer
given,
Dubois formula
[tex]S = 0.01 w^{0.25}h^{0.75}[/tex]
a) mass = 60 Kg
height = 1.6 m
[tex]S = 0.01 \times 60^{0.25}\times 160^{0.75}[/tex]
S = 1.252 m²
hence, surface area of a person is equal to 1.193 m² .
b) [tex]\dfrac{dw}{dt} = 0.4\ kg/year[/tex]
weight = 60 Kg
now,
[tex]\dfrac{dS}{dt} = 0.01(0.25)(\dfrac{h}{w})^{0.75}\dfrac{dw}{dt}[/tex]
[tex]\dfrac{dS}{dt} = 0.01(0.25)(\dfrac{160}{60})^{0.75}\times 0.4[/tex]
[tex]\dfrac{dS}{dt} = 0.00209\ m^2/year[/tex]
The surface area of the person using Dubois formula is 1.252 m².
The rate of change in the surface area of the person is 1.988 x 10⁻³ m²/year.
The surface area of the person can be determined using Dubois formula as shown below;
[tex]BSA = wt(kg)^{0.25} \times ht(cm)^{0.75} \times 0.01\\\\BSA = (60)^{0.25} \times 160^{0.75} \times 0.01\\\\BSA = 1.252 \ m^2[/tex]
The rate of change in the surface area of the person is calculated as follows;
[tex]\frac{d(BSA)}{dt} = 0.01 \times 0.25 \times (\frac{h}{w} )^{0.75} \times \frac{dw}{dt} \\\\\frac{d(BSA)}{dt} = 0.01 \times 0.25 \times (\frac{160}{64})^{0.75} \times 0.4\\\\\frac{d(BSA)}{dt} = 1.988 \times 10^{-3} \ m^2/year[/tex]
Learn more about surface area Dubois formula here: https://brainly.com/question/6897445
