Question

A model for the surface area of a human body is given by S = 0.1091w0.425h0.725, where w is the weight (in pounds), h is the height (in inches), and S is measured in square feet. If the errors in measurement of w and h are at most 2%, use differentials to estimate the maximum percentage error in the calcu- lated surface area.

Answer 1

Answer:

$2.3$%

Step-by-step explanation:

Surface area of a human body is given by -

$S = 0.1901* w^{0.425}* h^{0.725}$

Taking integral on both sides, we get -

$In S = 0.425 ln w + 0.725 ln h + ln 0.1091\\\frac{dS}{S} = 0.425\frac{dw}{w} + 0.725\frac{dh}{h}$

Since, the at most error in the surface area of a human body is $2$%

Substituting this in above equation, we get -

$\frac{dS}{S} \leq [0.425*0.02 + 0.725*0.02]\\\frac{dS}{S} \leq0.023$

Thus, the maximum error is surface area is equal to

$0.023 * 100\\= 2.3$%