Chapter 9.4, Problem 20E

Multivariable Calculus

Total Differentials and Approximations

LIFE SCIENCE APPLICATIONS

Heat Loss In Exercise $50$ of Section $2$ of this chapter, we found that the rate of heat loss (in watts) in harbor seal pups could be approximated by

$H\left(m,\text{ T, A}\right)=\frac{15.2m^{0.67}\left(T-A\right)}{10.23\ln m-10.74}$

Where $m$ is the body mass of the pup (in kg), and $T$ and $A$ are the body core temperature and

ambient water temperature, respectively (in $°C$). Suppose $m$ is $25\text{ kg}$, $T$ is ${36.0}^{\circ }$, and $A$ is ${12.0}^{\circ },$ Approximate the change in $H$ if $m$ changes to $26\text{ kg,}$ $T$ to ${36.5}^{\circ }$ and $A$ to ${10.0}^{\circ }.$