Chapter 3.4, Problem 50PS

Solution

Find the inverse of the model. Then estimate the height of a 60 kilogram person who has a body surface area of 1.6 square meters.

  $A^{-1}={\left(\frac{h}{0.2195}\right)}^{1/0.3964}$

Height = 149.30 centimeter.

Given information:

The body surface area A (in square meters) of a person with a mass of 60 kilogram can be approximated by the model $A=0.2195h^{0.3964}$ where h is the person’s height (in centimeters).

Concept used:

In order to find the inverse of a function $y=f\left(x\right)$, follow below steps:

Step 1: interchange x and y in the given function

Step 2: solve for y and that will give the required inverse function

Calculation:

The inverse of model $A=0.2195h^{0.3964}$ is -

  $\begin{array}{c}A=0.2195h^{0.3964}\\ y=A\\ y=0.2195h^{0.3964}\\ swaphwithy\\ h=0.2195y^{0.3964}\\ solvefory\\ h=0.2195y^{0.3964}\\ y^{0.3964}=\frac{h}{0.2195}\\ y={\left(\frac{h}{0.2195}\right)}^{1/0.3964}\\ A^{-1}={\left(\frac{h}{0.2195}\right)}^{1/0.3964}\end{array}$

Thus the inverse of the given function $A=0.2195h^{0.3964}$ is $A^{-1}={\left(\frac{h}{0.2195}\right)}^{1/0.3964}$ .

60kg Person who has a body surface area (A) of 1.6 square meters has height is-

  $A=0.2195h^{0.3964}$

  $\begin{array}{c}A=0.2195h^{0.3964}\\ 1.6=0.2195h^{0.3964}\\ \frac{1.6}{0.2195}=h^{0.3964}\\ h^{0.3964}=7.29\\ h={7.29}^{1/0.3964}\\ h=149.30\end{array}$

So 60kg person who has a body surface area (A) of 1.6 square meters has height = 149.30 centimeter.