Question

directions: use this information to answer parts a and b.
the function ( a(h) = 0.00718(m)^{0.425}(h)^{0.725} ) gives the area ( a ) (in square meters) of body surface where ( m ) is a person’s mass (in kilograms) and ( h ) is the person’s height (in centimeters). jake’s mass is 90.7 kg, and his body surface area is approximately ( 2.13 , \text{m}^2 ). use a graphing calculator to determine his height.

part a
state what strategy should be used to determine the height.
using the words into the boxes to correctly complete the sentence.
(show hints button here)
in the equation, ( a(h) = 0.00718(m)^{0.425}(h)^{0.725} ), substitute 90.7 for ( m ), 2.13 for ( a ), and rearrange the equation to solve for ( h ).

Explanation:

Step1: Identify known values

We know \( M = 90.7 \) kg, \( A = 2.13 \) \( m^2 \), and the formula \( A(H)=0.00718(M)^{0.425}(H)^{0.725} \).

Step2: Substitute known values

Substitute \( M = 90.7 \) for \( M \), \( A = 2.13 \) for \( A \) in the equation \( 2.13=0.00718\times(90.7)^{0.425}\times(H)^{0.725} \).

Step3: Solve for \( H \)

First, calculate \( 0.00718\times(90.7)^{0.425} \). Let's compute \( (90.7)^{0.425}\approx90.7^{0.425}\approx e^{0.425\ln(90.7)}\approx e^{0.425\times4.507}\approx e^{1.916}\approx6.79 \). Then \( 0.00718\times6.79\approx0.0488 \). So the equation becomes \( 2.13 = 0.0488\times(H)^{0.725} \). Then \( (H)^{0.725}=\frac{2.13}{0.0488}\approx43.65 \). Now, raise both sides to the power of \( \frac{1}{0.725} \), so \( H=(43.65)^{\frac{1}{0.725}}\approx(43.65)^{1.379}\approx e^{1.379\ln(43.65)}\approx e^{1.379\times3.78}\approx e^{5.21}\approx183. \) (using a calculator for more precise steps, but the strategy is substitution and solving for \( H \)).

Answer:

In the equation \( A(H) = 0.00718(M)^{0.425}(H)^{0.725} \), substitute \( 90.7 \) for \( M \), \( 2.13 \) for \( A \), and rearrange the equation to solve for \( H \). The strategy is substitution of known values (mass \( M \) and surface area \( A \)) into the formula and then algebraic manipulation to isolate and solve for height \( H \).